This specification defines a core subset of Mathematical Markup Language, or MathML, that is suitable for browser implementation. MathML is a markup language for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on the World Wide Web, just as HTML has enabled this functionality for text.
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Publication as a Working Draft does not imply endorsement by W3C and its Members.
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Table of ContentsMATH table
text-transform Mappings
bold-script mappingsbold-italic mappingstailed mappingsbold mappingsfraktur mappingsscript mappingsmonospace mappingsinitial mappingssans-serif mappingsdouble-struck mappingslooped mappingsstretched mappingsitalic mappingsbold-fraktur mappingssans-serif-bold-italic mappingssans-serif-italic mappingsbold-sans-serif mappingsThis section is non-normative.
The [MATHML3] specification has several shortcomings that make it hard to implement consistently across web rendering engines or to extend with user-defined constructions e.g.
This MathML Core specification intends to address these issues by being as accurate as possible on the visual rendering of mathematical formulas using additional rules from the TeXBookโs Appendix G [TEXBOOK] and from the Open Font Format [OPEN-FONT-FORMAT], [OPEN-TYPE-MATH-ILLUMINATED]. It also relies on modern browser implementations and web technologies [HTML] clarifying interactions with them when needed or introducing new low-level primitives to improve the web platform layering.
Parts of MathML3 that do not fit well in this framework or are less fundamental have been omitted. Instead, they are described in a separate and larger [MATHML4] specification. The details of which math feature will be included in future versions of MathML Core or implemented as polyfills is still open. This question and other potential improvements are tracked on GitHub.
By increasing the level of implementation details, focusing on a workable subset, following a browser-driven design and relying on automated web platform tests, this specification is expected to greatly improve MathML interoperability. Moreover, effort on MathML layering will enable users to implement the rest of the MathML 4 specification, or more generally to extend MathML Core, using modern web technologies such as shadow DOM, custom elements, CSS layout API or other Houdini APIs.
The term MathML element refers to any element in the MathML namespace. The MathML element defined in this specification are called the MathML Core elements and are listed below. Any MathML element that is not listed below is called an Unknown MathML element.
<annotation><annotation-xml><maction><math><merror><mfrac><mi><mmultiscripts><mn><mo><mover><mpadded><mphantom><mprescripts><mroot><mrow><ms><mspace><msqrt><mstyle><msub><msubsup><msup><mtable><mtd><mtext><mtr><munder><munderover><none><semantics>The grouping elements are <maction>, <math>, <merror> <mphantom>, <mprescripts>, <mrow>, <mstyle>, <none>, <semantics> and unknown MathML elements.
The scripted elements are <mmultiscripts>, <mover>, <msub>, <msubsup>, <msup>, <munder> and <munderover>.
The radical elements are <mroot> and <msqrt>.
The attributes defined in this specification have no namespace and are called MathML attributes:
maction attributesmo attributesmpadded attributesmspace attributesmunderover attributesmtd attributesencodingdisplaylinethicknessMathML specifies a single top-level or root <math> element, which encapsulates each instance of MathML markup within a document. All other MathML content must be contained in a <math> element.
The <math> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attribute:
The display attribute, if present, must be an ASCII case-insensitive match to block or inline. The user agent stylesheet described in A. User Agent Stylesheet contains rules for this attribute that affect the default values for the displayblock math or inline math) and math-stylenormal or compact) properties. If the display attribute is absent or has an invalid value, the User Agent stylesheet treats it the same as inline.
If the element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise the layout algorithm of the <mrow>display: block (if the computed value is block math) or display: inline (if the computed value is inline math). Additionally, if the computed display property is equal to block math then that MathML box is rendered horizontally centered within the content box.
Note
TEX's display mode $$...$$ and inline mode $...$ correspond to display="block" and display="inline" respectively.
In the following example, a <math> formula is rendered in display mode on a new line and taking full width, with the math content centered within the container:
<div style="width: 15em;">
This mathematical formula with a big summation and the number pi
<math display="block" style="border: 1px dotted black;">
<mrow>
<munderover>
<mo>โ</mo>
<mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow>
<mrow><mo>+</mo><mn>โ</mn></mrow>
</munderover>
<mfrac>
<mn>1</mn>
<msup><mi>n</mi><mn>2</mn></msup>
</mfrac>
</mrow>
<mo>=</mo>
<mfrac>
<msup><mi>ฯ</mi><mn>2</mn></msup>
<mn>6</mn>
</mfrac>
</math>
is easy to prove.
</div>As a comparison, the same formula would look as follows in inline mode. The formula is embedded in the paragraph of text without forced line breaking. The baselines specified by the layout algorithm of the <mrow>
Because good mathematical rendering requires use of mathematical fonts, the user agent stylesheet should set the font-family to the math value on the <math> element instead of inheriting it. Additionally, several CSS properties that can be set on a parent container such as font-style, font-weight, direction or text-indent etc are not expected to apply to the math formula and so the user agent stylesheet has rules to reset them by default.
math {
direction: ltr;
writing-mode: horizontal-tb;
text-indent: 0;
letter-spacing: normal;
line-height: normal;
word-spacing: normal;
font-family: math;
font-size: inherit;
font-style: normal;
font-weight: normal;
display: inline math;
math-style: compact;
math-shift: normal;
math-level: 0;
}
math[display="block" i] {
display: block math;
math-style: normal;
}
math[display="inline" i] {
display: inline math;
math-style: compact;
}<integer> value as defined in [CSS-VALUES-3], whose first character is neither U+002D HYPHEN-MINUS character (-) nor U+002B PLUS SIGN (+).
<length-percentage> value as defined in [CSS-VALUES-3]
<color> value as defined in [CSS-COLOR-3]
true or false.
The following attributes are common to and may be specified on all MathML elements:
classdata-*dirdisplaystyleidmathbackgroundmathcolormathsizemathvariantnoncescriptlevelstyletabindexon* event handler attributesThe id, class, style, data-*, nonce and tabindex attributes have the same syntax and semantic as defined for id, class, style, data-*, nonce and tabindex attributes on HTML elements.
The dir attribute, if present, must be an ASCII case-insensitive match to ltr or rtl. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's direction property to the corresponding value. More precisely, an ASCII case-insensitive match to rtl is mapped to rtl while an ASCII case-insensitive match to ltr is mapped to ltr.
Note
The
dir
attribute is used to set the directionality of math formulas, which is often
rtl
in Arabic speaking world. However, languages written from right to left often embed math written from left to right and so the
user agent stylesheetresets the
direction
property accordingly on the
<math>elements.
In the following example, the dir attribute is used to render "๐ธ plus ๐ธ raised to the power of (ูข over, ๐ธ plus ูก)" from right-to-left.
<math dir="rtl">
<mrow>
<mi>๐ธ</mi>
<mo>+</mo>
<msup>
<mi>๐ธ</mi>
<mfrac>
<mn>ูข</mn>
<mrow>
<mi>๐ธ</mi>
<mo>+</mo>
<mn>ูก</mn>
</mrow>
</mfrac>
</msup>
</mrow>
</math>All MathML elements support event handler content attributes, as described in event handler content attributes in HTML.
All event handler content attributes noted by HTML as being supported by all HTMLElements are supported by all MathML elements as well, as defined in the MathMLElement IDL.
The mathcolor and mathbackground attributes, if present, must have a value that is a color. In that case, the user agent is expected to treat these attributes as a presentational hint setting the element's color and background-color properties to the corresponding values. The mathcolor attribute describes the foreground fill color of MathML text, bars etc while the mathbackground attribute describes the background color of an element.
The mathsize attribute, if present, must have a value that is a valid length-percentage. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's font-size property to the corresponding value. The mathsize property indicates indicates the desired height of glyphs in math formulas but also scale other parts (spacing, shifts, line thickness of bars etc) accordingly.
Note
The above attributes are implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use CSS for styling.
The mathvariant attribute, if present, must be an ASCII case-insensitive match to one of: normal, bold, italic, bold-italic, double-struck, bold-fraktur, script, bold-script, fraktur, sans-serif, bold-sans-serif, sans-serif-italic, sans-serif-bold-italic, monospace, initial, tailed, looped, or stretched. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's text-transformnormal is mapped to none while any other valid value is mapped to its ASCII lowercased value, prefixed with math-.
The mathvariant attribute defines logical classes of token elements. Each class provides a collection of typographically-related symbolic tokens with specific meaning within a given mathematical expression. For mathvariant values other than normal, this is done by using glyphs of Mathematical Alphanumeric Symbols [UNICODE].
In the following example, the mathvariant attribute is used to render different A letters. Note that by default variables use mathematical italic.
<math>
<mi>A</mi>
<mi mathvariant="normal">A</mi>
<mi mathvariant="fraktur">A</mi>
<mi mathvariant="double-struck">A</mi>
</math>Note
mathvariant
values other than
normal
are implemented for compatibility with full MathML and legacy editors that can't access characters in Plane 1 of Unicode. Authors are encouraged to use the corresponding Unicode characters. The
normal
value is still important to cancel automatic italic of the
<mi>element.
Note
It is sometimes needed to distinguish between Chancery and Roundhand style for MATHEMATICAL SCRIPT characters. These are notably used in LaTeX for the \mathcal and \mathscr commands.
One way to do that is to rely on Chapter 23.4 Variation Selectors of Unicode which describes a way to specify selection of particular glyph variants [UNICODE]. Indeed, the StandardizedVariants.txt file from the Unicode Character Database indicates that variant selectors U+FE00 and U+FE01 can be used on capital script to specify Chancery and Roundhand respectively.
Alternatively, some mathematical fonts rely on salt or ssXY properties from [OPEN-FONT-FORMAT] to provide both styles. Page authors may use the font-variant-alternates property with corresponding OpenType font features to access these glyphs.
The displaystyle attribute, if present, must have a value that is a boolean. In that case, the user agent is expected to treat the attribute as a presentational hint setting the element's math-styletrue is mapped to normal while an ASCII case-insensitive match to false is mapped to compact. This attribute indicates whether formulas should try to minimize the logical height (value is false) or not (value is true) e.g. by changing the size of content or the layout of scripts.
The scriptlevel attribute, if present, must have value +<U>, -<U> or <U> where <U> is an unsigned-integer. In that case the user agent is expected to treat the scriptlevel attribute as a presentational hint setting the element's math-depth+<U>, -<U> and <U> are respectively mapped to add(<U>) add(<-U>) and <U>.
displaystylescriptlevelfont-size: math is specified to ensure that scriptlevel changes are taken into account.
In this example, a <munder> element is used to attach a script "A" to a base "โ". By default, the summation symbol is rendered with the font-size inherited from its parent and the A as a scaled down subscript. If displaystyle is true, the summation symbol is drawn bigger and the "A" becomes an underscript. If scriptlevel is reset to 0 on the "A", then it will use the same font-size as the top-level math root.
<math>
<munder>
<mo>โ</mo>
<mi>A</mi>
</munder>
<munder displaystyle="true">
<mo>โ</mo>
<mi>A</mi>
</munder>
<munder>
<mo>โ</mo>
<mi scriptlevel="0">A</mi>
</munder>
</math>Note
T
EX's
\displaystyle
,
\textstyle
,
\scriptstyle
, and
\scriptscriptstyle
correspond to
displaystyleand
scriptlevelas
true
and
0
,
false
and
0
,
false
and
1
, and
false
and 2, respectively.
When parsing HTML documents user agents must treat any tag name corresponding to a MathML Core Element as belonging to the MathML namespace.
Users agents must allow mixing HTML, SVG and MathML elements as allowed by sections HTML integration point, MathML integration point, tree construction dispatcher, MathML and SVG from [HTML].
When evaluating the SVG requiredExtensions attribute, user agents must claim support for the language extension identified by the MathML namespace.
In this example, inline MathML and SVG elements are used inside a HTML document. SVG elements <switch> and <foreignObject> (with proper <requiredExtensions>) are used to embed a MathML formula with a text fallback, inside a diagram. HTML input element is used within the <mtext> include an interactive input field inside a mathematical formula.
<svg style="font-size: 20px" width="400px" height="220px" viewBox="0 0 200 110">
<g transform="translate(10,80)">
<path d="M 0 0 L 150 0 A 75 75 0 0 0 0 0
M 30 0 L 30 -60 M 30 -10 L 40 -10 L 40 0"
fill="none" stroke="black"></path>
<text transform="translate(10,20)">1</text>
<switch transform="translate(35,-40)">
<foreignObject width="200" height="50"
requiredExtensions="http://www.w3.org/1998/Math/MathML">
<math>
<msqrt>
<mn>2</mn>
<mi>r</mi>
<mo>โ</mo>
<mn>1</mn>
</msqrt>
</math>
</foreignObject>
<text>\sqrt{2r - 1}</text>
</switch>
</g>
</svg>
<p>
Fill the blank:
<math>
<msqrt>
<mn>2</mn>
<mtext><input onchange="..." size="2" type="text"></mtext>
<mo>โ</mo>
<mn>1</mn>
</msqrt>
<mo>=</mo>
<mn>3</mn>
</math>
</p>User agents must support various CSS features mentioned in this specification, including new ones described in 4. CSS Extensions for Math Layout. They must follow the computation rule for display: contents.
In this example, the MathML formula inherits the CSS color of its parent and uses the font-family specified via the style attribute.
<div style="width: 15em; color: blue">
This mathematical formula with a big summation and the number pi
<math display="block" style="font-family: STIX Two">
<mrow>
<munderover>
<mo>โ</mo>
<mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow>
<mrow><mo>+</mo><mn>โ</mn></mrow>
</munderover>
<mfrac>
<mn>1</mn>
<msup><mi>n</mi><mn>2</mn></msup>
</mfrac>
</mrow>
<mo>=</mo>
<mfrac>
<msup><mi>ฯ</mi><mn>2</mn></msup>
<mn>6</mn>
</mfrac>
</math>
is easy to prove.
</div>All documents containing MathML Core elements must include CSS rules described in A. User Agent Stylesheet as part of user-agent level style sheet defaults.
The following CSS features are not supported and must be ignored:
writing-mode is treated as horizontal-tb on all MathML elements.white-space is treated as nowrap on all MathML elements.width, height, inline-size and block-size are treated as auto on elements with computed display value block math or inline math.float and clear are treated as none on all MathML elements.align-content, justify-content, align-self, justify-self have no effect on MathML elements.Note
These features might be handled in future versions of this document. For now, authors are discouraged from setting a different value for these properties as that might lead to backward incompatibility issues.
User agents supporting Web application APIs must ensure that they keep the visual rendering of MathML synchronized with the [DOM] tree, in particular perform necessary updates when MathML attributes are modified dynamically.
All the nodes representing MathML elements in the DOM must implement, and expose to scripts, the following MathMLElement interface.
[Exposed=Window]
interface MathMLElement : Element { };
MathMLElement includes GlobalEventHandlers;
MathMLElement includes DocumentAndElementEventHandlers;
MathMLElement includes HTMLOrForeignElement;The GlobalEventHandlers, DocumentAndElementEventHandlers and HTMLOrForeignElement interfaces are defined in [HTML].
Each IDL attribute of the MathMLElement interface reflects the corresponding MathML content attribute.
In the following example, a MathML formula is used to render the fraction "ฮฑ over 2". When clicking the red ฮฑ, it is changed into a blue ฮฒ.
<script>
function ModifyMath(mi) {
mi.style.color = 'blue';
mi.textContent = 'ฮฒ';
}
</script>
<math>
<mrow>
<mfrac>
<mi style="color: red" onclick="ModifyMath(this)">ฮฑ</mi>
<mn>2</mn>
</mfrac>
</mrow>
</math>Because math fonts generally contain very tall glyphs such as big integrals, using typographic metrics is important to avoid excessive line spacing of text. As a consequence, user agents must take into account the USE_TYPO_METRICS flag from the OS/2 table [OPEN-FONT-FORMAT] when performing text layout.
MathML provides the ability for authors to allow for interactivity in supporting interactive user agents using the same concepts, approach and guidance to Focus as described in HTML, with modifications or clarifications regarding application for MathML as described in this section.
When an element is focused, all applicable CSS focus-related pseudo-classes as defined in Selectors Level 3 apply, as defined in that specification.
The contents of embedded <math>
The default display property is described in A. User Agent Stylesheet:
<math> root, it is equal to inline math or block math according to the value of the display attribute.<mtable><mtr><mtd>inline-table, table-row and table-cell.<maction> and <semantics> elements, it is equal to none.block math.In order to specify math layout in different writing modes, this specification uses concepts from [CSS-WRITING-MODES-3]:
Note
Unless specified otherwise, the figures in this specification use a
writing modeof
horizontal-lr
and
ltr
. See
Figure 4,
Figure 5and
Figure 6for examples of other writing modes that are sometimes used for math layout.
MathML boxes have several parameters in order to perform layout in a way that is compatible with CSS but also to take into account very accurate positions and spacing within math formulas. Each math box has the following parameters:
Block metrics. The block size, first baseline set and last baseline set. The following baselines are defined for MathML boxes:
Note
For math layout, it is very important to rely on the ink extent when positioning text. This is not the case for more complex notations (e.g. square root). Although ink-ascent and ink-descent are defined for all MathML elements they are really only used for the token elements. In other cases, they just match normal ascent and descent.
Unless specified otherwise, the last baseline set is equal to the first baseline set for MathML boxes.Given a MathML box, the following offsets are defined:
horizontal-tb and rtl that may be used in e.g. Arabic math. Figure 5 Box model for writing mode vertical-lr and ltr that may be used in e.g. Mongolian math. Figure 6 Box model for writing mode vertical-rl and ltr that may be used in e.g. Japanese math.
Note
The position of child boxes and graphical items inside a MathML box are expressed using the
inline offsetand
block offset. For convenience, the layout algorithms may describe offsets using flow-relative directions, line-relative directions or the
alphabetic baseline. It is always possible to pass from one description to the other because position of child boxes are always performed after the metrics of the box and of its child boxes are calculated.
Improve definition of ink ascent/descent?
The layout algorithms described in this chapter for MathML boxes have the following structure:
During box layout, the following extra steps must be performed:
The box metrics and offsets of the padding box are obtained from the content box by taking into account the corresponding padding properties as described in CSS.
The baselines of the padding box are the same as the one of the content box.
If the content box has a top accent attachment then the padding box has the same property, increased by the inline-start padding. If the content box has an italic correction then the padding box has the same property, increased by the inline-end padding.
The box metrics and offsets of the border box are obtained from the padding box by taking into account the corresponding border-width property as described in CSS.
In general, the baselines of the border box are the same as the one of the padding box. However, if the line-over border is positive then the ink-over baseline is set to the line-over edge of the border box and if the line-under border is positive then the ink-under baseline is set to the line-under edge of the border box.
If the padding box has a top accent attachment then the border box has the same property, increased by the border-width of its inline-start egde. If the padding box has an italic correction then the border box has the same property, increased by the border-width of its inline-end egde.
The box metrics and offsets of the margin box are obtained from the border box by taking into account the corresponding margin properties as described in CSS.
The baselines of the margin box are the same as the one of the border box.
If the padding box has a top accent attachment then the margin box has the same property, increased by the inline-start margin. If the padding box has an italic correction then the margin box has the same property, increased by the inline-end margin.
During box layout, optional inline stretch size constraint and block stretch size constraint parameters may be used on embellished operators. The former indicates a target size that a core operator stretched along the inline axis should cover. The latter indicates an ink line-ascent and ink line-descent that a core operator stretched along the block axis should cover. Unless specified otherwise, these parameters are ignored during box layout and child boxes are laid out without any stretch size constraint.
Explain how out-of-flow elements are positioned.
Interpret width/height/inline-size/block-size?
Define what inline percentages resolve against
Define what block percentages resolve against
MathML elements can overlap due to various spacing rules. They can as well contain extra graphical items (bars, radical symbol, etc). A MathML element with computed style display: block math or display: inline math generates a new stacking context. The painting order of in-flow children of such a MathML element is exactly the same as block elements. The extra graphical items are painted after text and background (right after step 7.2.4 for display: inline math and right after step 7.2 for display: block math).
Token elements in presentation markup are broadly intended to represent the smallest units of mathematical notation which carry meaning. Tokens are roughly analogous to words in text. However, because of the precise, symbolic nature of mathematical notation, the various categories and properties of token elements figure prominently in MathML markup. By contrast, in textual data, individual words rarely need to be marked up or styled specially.
Note
In practice, most MathML token elements just contain simple text for variables, numbers, operators etc and don't need sophisticated layout. However, it can contain contain text with line breaks or arbitrary HTML5 phrasing elements.
The <mtext> element is used to represent arbitrary text that should be rendered as itself. In general, the <mtext> element is intended to denote commentary text.
The <mtext> element accepts the attributes described in 2.1.3 Global Attributes.
In the following example, <mtext> is used to put conditional words in a definition:
<math>
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mtext> if </mtext>
<mrow>
<mi>x</mi>
<mo>โฅ</mo>
<mn>1</mn>
</mrow>
<mtext> and </mtext>
<mn>2</mn>
<mtext> otherwise.</mtext>
</mrow>
</math>If the element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
The mtext element is laid out as a block box and the min-content inline size, max-content inline size, inline size, block size, first baseline set and last baseline set are determined accordingly.
If the <mtext> element contains only text content without forced line break or soft wrap opportunity then in addition:
<mtext> element.The <mi> element represents a symbolic name or arbitrary text that should be rendered as an identifier. Identifiers can include variables, function names, and symbolic constants.
The <mi> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mtext> element. The user agent stylesheet must contain the following property in order to implement automatic italic:
mi {
text-transform: math-auto;
}In the following example, <mi> is used to render variables and function names. Note that identifiers containing a single letter are italic by default.
<math>
<mi>cos</mi>
<mo>,</mo>
<mi>c</mi>
<mo>,</mo>
<mi mathvariant="normal">c</mi>
</math>The <mn> element represents a "numeric literal" or other data that should be rendered as a numeric literal. Generally speaking, a numeric literal is a sequence of digits, perhaps including a decimal point, representing an unsigned integer or real number.
The <mn> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mtext>
In the following example, <mn> is used to write a decimal number.
<math>
<mn>3.141592653589793</mn>
</math>The <mo> element represents an operator or anything that should be rendered as an operator. In general, the notational conventions for mathematical operators are quite complicated, and therefore MathML provides a relatively sophisticated mechanism for specifying the rendering behavior of an <mo> element.
As a consequence, in MathML the list of things that should "render as an operator" includes a number of notations that are not mathematical operators in the ordinary sense. Besides ordinary operators with infix, prefix, or postfix forms, these include fence characters such as braces, parentheses, and "absolute value" bars; separators such as comma and semicolon; and mathematical accents such as a bar or tilde over a symbol. This chapter uses the term "operator" to refer to operators in this broad sense.
The <mo> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:
This specification does not define any observable behavior that is specific to the fence and separator attributes.
In the following example, the <mo> element is used for the binary operator +. Default spacing is symmetric around that operator. A tigher spacing is used if you rely on the formlspacerspace
<math>
<mn>1</mn>
<mo>+</mo>
<mn>2</mn>
<mo form="prefix">+</mo>
<mn>3</mn>
<mo lspace="2em">+</mo>
<mn>4</mn>
<mo rspace="3em">+</mo>
<mn>5</mn>
</math>Another use case is for big operator such as summation. When displaystyle is true, such an operator are drawn larger but one can change that with the largeop attribute. When displaystyle is false, underscript are actually rendered as subscript but one can change that with the movablelimits attribute.
<math>
<mrow displaystyle="true">
<munder>
<mo>โ</mo>
<mn>5</mn>
</munder>
<munder>
<mo largeop="false">โ</mo>
<mn>6</mn>
</munder>
</mrow>
<mrow>
<munder>
<mo>โ</mo>
<mn>5</mn>
</munder>
<munder>
<mo movablelimits="false">โ</mo>
<mn>7</mn>
</munder>
</mrow>
</math>Operators are also used for stretchy symbols such as fences, accents, arrows etc. In the following example, the vertical arrow stretches to the height of the <mspace> element. One can override default stretch behavior with the stretchy attribute e.g. to force an unstretched arrow. The symmetric attribute allows to indicate whether the operator should stretchy symmetrically above and below the baseline. Finally the minsize and maxsize attributes add additional constraints over the stretch size.
<math>
<mspace height="100px" width="10px" style="background: blue"/>
<mo>โ</mo>
<mo stretchy="false">โ</mo>
<mo symmetric="true">โ</mo>
<mo minsize="150px">โ</mo>
<mo maxsize="50px">โ</mo>
</math>Note that the default properties of operators are dictionary-based, as explained in 3.2.4.2 Dictionary-based attributes. For example a binary operator typically has default symmetric spacing around it while a fence is generally stretchy by default.
A MathML Core element is an embellished operator if it is:
<mo><mfrac><mpadded>, whose in-flow children consist (in any order) of one embellished operator and zero or more space-like elements.The core operator of an embellished operator is the <mo> element defined recursively as follows:
<mo><mfrac><mpadded> is the core operator of its unique embellished operator in-flow child.The stretch axis of an embellished operator is inline if its core operator contains only text content made of a unique character c, and that character has inline intrinsic stretch axis. Otherwise, the stretch axis of the embellished operator is block.
The form property of an embellished operator is either infix, prefix or postfix. The corresponding form attribute on the <mo>
The algorithm for determining the form of an embellished operator is as follows:
form attribute is present and valid on the core operator, then its ASCII lowercased value is used;<mpadded> or <msqrt> with more than one in-flow child (ignoring all space-like children) then it has form prefix;<mpadded><msqrt>postfix;postfix;infix.The stretchy, symmetric, largeop, movablelimits, properties of an embellished operator are either false or true. In the latter case, it is said that the embellished operator has the property. The corresponding attributes on the <mo>
The lspace, rspace, minsize properties of an embellished operator are length-percentage. The maxsize property of an embellished operator is either a length-percentage or โ. The lspace, rspace, minsize and maxsize attributes on the <mo>
The algorithm for determining the properties of an embellished operator is as follows:
stretchy, symmetric, largeop, movablelimits, lspace, rspace, maxsize or minsize attribute is present and valid on the core operator, then the ASCII lowercased value of this property is used;form of an embellished operator;Content, then set Category to the result of the algorithm to determine the category of an operator (Content, Form) where Form is the formCategory is Default and the formCategory to the result of the algorithm to determine the category of an operator (Content, Form) where Form is infix.Category is Default, then run the algorithm again with Form set to prefix.Category is Default, then run the algorithm again with Form set to postfix.Category.When used during layout, the values of stretchysymmetriclargeopmovablelimitslspacerspaceminsize
lspace, rspace are interpreted relative to the value read from the dictionary or to the fallback value above.minsize and maxsize are described in 3.2.4.3 Layout of operators.lspace, rspace, minsize and maxsize rely on the font style of the core operator, not the one of the embellished operator.If the <mo> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
The text of the operator must only be painted if the visibility of the <mo> element is visible. In that case, it must be painted with the color of the <mo> element.
Operators are laid out as follows:
<mo> element is not made of a single character c then fallback to the layout algorithm of 3.2.1.1 Layout of <mtext>.stretchy property:
c in the inline direction with the first available font then fallback to the layout algorithm of 3.2.1.1 Layout of <mtext>.<mtext>.Tinline then fallback to the layout algorithm of 3.2.1.1 Layout of <mtext>.Tinline.Tinline and at position determined by the previous box metrics.c in the block direction with the first available font then fallback to the layout algorithm of 3.2.1.1 Layout of <mtext>.(Uascent, Udescent) then fallback to the layout algorithm of 3.2.1.1 Layout of <mtext>.symmetric property then set the target sizes Tascent and Tdescent to Sascent and Sdescent respectively:
Sascent = max( Uascent โ AxisHeight, Udescent + AxisHeight ) + AxisHeightSdescent = max( Uascent โ AxisHeight, Udescent + AxisHeight ) โ AxisHeightUascent and Udescent respectively.minsize and maxsize be the minsize and maxsize properties on the operator. Percentage values are intepreted relative to T = Tascent + Tdescent. If minsize < 0 then set minsize to 0. If maxsize < minsize then set maxsize to minsize. Then 0 โค minsize โค maxsize:
T โค 0 then set Tascent to minsize / 2 and then set Tdescent to minsize โ TascentT < minsize then first multiply Tascent by minsize / T and then set Tdescent to minsize - Tascent.maxsize < T then first multiply Tascent by maxsize / T and then set Tdescent to maxsize โ Tascent.Tascent + Tdescent. The inline size of the content is the width of the stretchy glyph. The stretchy glyph is shifted towards the line-under by a value ฮ so that its center aligns with the center of the target: the ink ascent of the content is the ascent of the stretchy glyph โ ฮ and the ink descent of the content is the descent of the stretchy glyph + ฮ. These centers have coordinates "ยฝ(ascent โ descent)" so ฮ = [(ascent of stretchy glyph โ descent of stretchy glyph) โ (Tascent โ Tdescent)] / 2.Tascent + Tdescent and at position determined by the previous box metrics shifted by ฮ towards the line-over.largeop property and if math-style<mo> element is normal, then:
Use the MathVariants table to try and find a glyph of height at least DisplayOperatorMinHeight If none is found, fallback to the largest non-base glyph. If none is found, fallback to the layout algorithm of 3.2.1.1 Layout of <mtext>.
<mtext>.If the algorithm to shape a stretchy glyph has been used for one of the step above, then the italic correction of the content is set to the value returned by that algorithm.
Note
If maxsize is equal to its default value โ then minsize โค maxsize is satisfied but maxsize < T is not.
The <mspace> empty element represents a blank space of any desired size, as set by its attributes.
The <mspace> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:
The mspace@width, mspace@height, mspace@depth, if present, must have a value that is a valid length-percentage. An unspecified attribute, a percentage value, or an invalid value is interpreted as 0. If one of the requested values calculated is negative then it is treated as 0.
In the following example, <mspace> is used to force spacing within the formula (a 1px blue border is added to easily visualize the space):
<math>
<mn>1</mn>
<mspace width="1em"
style="border-top: 1px solid blue"/>
<mfrac>
<mrow>
<mn>2</mn>
<mspace depth="1em"
style="border-left: 1px solid blue"/>
</mrow>
<mrow>
<mn>3</mn>
<mspace height="2em"
style="border-left: 1px solid blue"/>
</mrow>
</mfrac>
</math>If the <mspace> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the <mspace> element is laid out as shown on Figure 9. The min-content inline size and max-content inline size of the content are equal to the requested inline size. The inline size, line-ascent and line-descent of the content are respectively the requested inline size, line-ascent and line-descent.
<mspace> element
Note
The terminology height/depth comes from [
MATHML3], itself inspired from [
TEXBOOK].
A number of MathML presentation elements are "space-like" in the sense that they typically render as whitespace, and do not affect the mathematical meaning of the expressions in which they appear. As a consequence, these elements often function in somewhat exceptional ways in other MathML expressions.
A MathML Core element is a space-like element if it is:
<mtext><mspace><mpadded> all of whose in-flow children are space-like.Note
Note that an
<mphantom>is not automatically defined to be space-like, unless its content is space-like. This is because operator spacing is affected by whether adjacent elements are space-like. Since the
<mphantom>
element is primarily intended as an aid in aligning expressions, operators adjacent to an
<mphantom>
should behave as if they were adjacent to the contents of the
<mphantom>
, rather than to an equivalently sized area of whitespace.
<ms> element is used to represent "string literals" in expressions meant to be interpreted by computer algebra systems or other systems containing "programming languages".
The <ms> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mtext>
In the following example, <ms> is used to write a literal string of characters:
<math>
<mi>s</mi>
<mo>=</mo>
<ms>"hello world"</ms>
</math>Note
In MathML3, it was possible to use the
lquote
and
rquote
attributes to respectively specify the strings to use as opening and closing quotes. These are no longer supported and the quotes must instead be specified as part of the text of the
<ms>
element. One can add CSS rules to legacy documents in order to preserve visual rendering. For example, in left-to-right direction:
ms:before, ms:after {
content: "\0022";
}
ms[lquote]:before {
content: attr(lquote);
}
ms[rquote]:after {
content: attr(rquote);
}Besides tokens there are several families of MathML presentation elements. One family of elements deals with various "scripting" notations, such as subscript and superscript. Another family is concerned with matrices and tables. The remainder of the elements, discussed in this section, describe other basic notations such as fractions and radicals, or deal with general functions such as setting style properties and error handling.
The <mrow> element is used to group together any number of sub-expressions, usually consisting of one or more <mo> elements acting as "operators" on one or more other expressions that are their "operands".
In the following example, <mrow> is used to group a sum "1 + 2/3" as a fraction numerator (first child of <mfrac>) and to construct a fenced expression (first child of <msup>) that is raised to the power of 5. Note that <mrow> alone does not add visual fences around its grouped content, one has to explicitly specify them using the <mo> element.
Within the <mrow> elements, one can see that vertical alignment of children (according to the alphabetic baseline or the mathematical baseline) is properly performed, fences are vertically stretched and spacing around the binary + operator automatically calculated.
<math>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mn>4</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mn>5</mn>
</msup>
</math>The <mrow> element accepts the attributes described in 2.1.3 Global Attributes. An <mrow> element with in-flow children child1, child2, โฆ childN is laid out as show on Figure 10. The child boxes are put in a row one after the other with all their alphabetic baselines aligned.
<mrow> element Figure 11 Symmetric and non-symmetric stretching of operators along the block axis
The algorithm for stretching operators along the block axis consists in the following steps:
LToStretch containing embellished operators with a stretchy property and block stretch axis ; and a second list LNotToStretch.LNotToStretch. If LToStretch is empty then stop. If LNotToStretch is empty, perform layout with stretch size constraint 0 on all the items of LToStretch.Uascent and Udescent as respectively the maximum ink ascent and maximum ink descent of the margin boxes of in-flow children that have been laid out in the previous step.LToStretch with block stretch size constraint (Uascent, Udescent).If the element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
A child box is slanted if it is not an embellished operator and has nonzero italic correction.
The min-content inline size (respectively max-content inline size) are calculated using the following algorithm:
add-space to true if the element is a <math> or is not an embellished operator; and to false otherwise.inline-offset to 0.previous-italic-correction to 0.inline-offset by previous-italic-correction.add-space is true then increment inline-offset by its lspaceinline-offset by the min-content inline size (respectively max-content inline size) of the child's margin box.previous-italic-correction to its italic correction. Otherwise set it to 0.add-space is true then increment inline-offset by its rspaceinline-offset by previous-italic-correction.inline-offset.The in-flow children are laid out using the algorithm for stretching operators along the block axis.
The inline size of the content is calculated like the min-content inline size and max-content inline size of the content, using the inline size of the in-flow children's margin boxes instead.
The ink line-ascent (respectively line-ascent) of the content is the maximum of the ink line-ascents (respectively line-ascents) of all the in-flow children's margin boxes. Similarly, the ink line-descent (respectively line-descent) of the content is the maximum of the ink line-descents (respectively ink line-ascents) of all the in-flow children's margin boxes.
The in-flow children are positioned using the following algorithm:
add-space to true if the element is a <math> or is not an embellished operator; and to false otherwise.inline-offset to 0.previous-italic-correction to 0.inline-offset by previous-italic-correction.add-space is true then increment inline-offset by its lspaceinline-offset and its block offset such that the alphabetic baseline of the child is aligned with the alphabetic baseline.inline-offset by the inline size of the child's margin box.previous-italic-correction to its italic correction. Otherwise set it to 0.add-space is true then increment inline-offset by its rspaceThe italic correction of the content is set to the italic correction of the last in-flow child, which is the final value of previous-italic-correction.
The <mfrac> element is used for fractions. It can also be used to mark up fraction-like objects such as binomial coefficients and Legendre symbols.
If the <mfrac> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
The <mfrac> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attribute:
The linethickness attribute indicates the fraction line thickness to use for the fraction bar. If present, it must have a value that is a valid length-percentage. If the attribute is absent or has an invalid value, FractionRuleThickness is used as the default value. A percentage is interpreted relative to that default value. A negative value is interpreted as 0.
The following example contains four fractions with different linethickness values. The bars are always aligned with the middle of plus and minus signs. The numerator and denominator are horizontally centered. The fractions that are not in displaystyle use smaller gaps and font-size.
<math>
<mn>0</mn>
<mo>+</mo>
<mfrac displaystyle="true">
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>โ</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mfrac linethickness="200%">
<mn>1</mn>
<mn>234</mn>
</mfrac>
<mo>โ</mo>
<mrow>
<mo>(</mo>
<mfrac linethickness="0">
<mn>123</mn>
<mn>4</mn>
</mfrac>
<mo>)</mo>
</mrow>
</math>The <mfrac> element sets displaystylefalse, or if it was already false increments scriptlevelmath-shift to compact within its second child. To avoid visual confusion between the fraction bar and another adjacent items (e.g. minus sign or another fraction's bar), a default 1-pixel space is added around the element. The user agent stylesheet must contain the following rules:
mfrac {
padding-inline-start: 1px;
padding-inline-end: 1px;
}
mfrac > * {
math-depth: auto-add;
math-style: compact;
}
mfrac > :nth-child(2) {
math-shift: compact;
}If the <mfrac> element has less or more than two in-flow children, its layout algorithm is the same as the <mrow>
If the fraction line thickness is nonzero, the <mfrac> element is laid out as shown on Figure 12. The fraction bar must only be painted if the visibility of the <mfrac> element is visible. In that case, the fraction bar must be painted with the color of the <mfrac> element.
<mfrac> element
The min-content inline size (respectively max-content inline size) of content is the maximum between the min-content inline size (respectively max-content inline size) of the numerator's margin box and the min-content inline size (respectively max-content inline size) of the denominator's margin box.
If there is an inline stretch size constraint or a block stretch size constraint then the numerator is also laid out with the same stretch size constraint otherwise it is laid out without any stretch size constraint. The denominator is always laid out without any stretch size constraint.
The inline size of the content is the maximum between the inline size of the numerator's margin box and the inline size of the denominator's margin box.
NumeratorShift is the maximum between:
math-style is compact (respectively normal).math-style is compact (respectively normal) + the ink line-descent of the numerator's margin box.DenominatorShift is the maximum between:
math-style is compact (respectively normal).math-style is compact (respectively normal) + the ink line-ascent of the denominator's margin box โ the AxisHeight.The line-ascent of the content is the maximum between:
Numerator Shift + the line-ascent of the numerator's margin box.Denominator Shift + the line-ascent of the denominator's margin boxThe line-descent of the content is the maximum between:
Numerator Shift + the line-descent of the numerator's margin box.Denominator Shift + the line-descent of the denominator's margin box.The inline offset of the numerator (respectively denominator) is the half the inline size of the content โ half the inline size of the numerator's margin box (respectively denominator's margin box).
The alphabetic baseline of the numerator (respectively denominator) is shifted away from the alphabetic baseline by a distance of NumeratorShift (respectively DenominatorShift ) towards the line-over (respectively line-under).
The inline size of the fraction bar is the inline size of the content and its inline offset is 0. The center of the fraction bar is shifted away from the alphabetic baseline by a distance of AxisHeight towards the line-over. Its block size is the fraction line thickness.
If the fraction line thickness is zero, the <mfrac> element is instead laid out as shown on Figure 13.
<mfrac> element without bar
The min-content inline size, max-content inline size and inline size of the content are calculated the same as in 3.3.2.1 Fraction with nonzero line thickness.
If there is an inline stretch size constraint or a block stretch size constraint then the numerator is also laid out with the same stretch size constraint and otherwise it is laid out without any stretch size constraint. The denominator is always laid out without any stretch size constraint.
If the math-style is compact then TopShift and BottomShift are respectively set to StackTopShiftUp and StackBottomShiftDown. Otherwise math-style is normal and they are respectively set to StackTopDisplayStyleShiftUp and StackBottomDisplayStyleShiftDown.
The Gap is defined to be (BottomShift โ the ink line-ascent of the denominator's margin box) + (TopShift โ the ink line-descent of the numerator's margin box). If math-style is compact then GapMin is StackGapMin otherwise math-style is normal and it is StackDisplayStyleGapMin. If ฮ = GapMin โ Gap is positive then TopShift and BottomShift are respectively increased by ฮ/2 and ฮ โ ฮ/2.
The line-ascent of the content is the maximum between:
TopShift + the line-ascent of the numerator's margin box.BottomShift + the line-ascent of the denominator's margin box.The line-descent of the content is the maximum between:
TopShift + the line-descent of the numerator's margin box.BottomShift + the line-descent of the denominator's margin box.The inline offsets of the numerator and denominator are calculated the same as in 3.3.2.1 Fraction with nonzero line thickness.
The alphabetic baseline of the numerator (respectively denominator) is shifted away from the alphabetic baseline by a distance of TopShift (respectively โ BottomShift) towards the line-over (respectively line-under).
The radical elements construct an expression with a root symbol โ with a line over the content. The <msqrt> element is used for square roots, while the <mroot> element is used to draw radicals with indices, e.g. a cube root.
The <msqrt> and <mroot> elements accept the attributes described in 2.1.3 Global Attributes.
The following example contains a square root written with <msqrt> and a cube root written with <mroot>. Note that <msqrt> has several children and the square root applies to all of them. <mroot> has exactly two children: it is a root of index the second child (the number 3), applied to the first child (the square root). Also note these elements only change the font-size within the <mroot> index, but it is scaled down more than within the numerator and denumerator of the fraction.
<math>
<mroot>
<msqrt>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>4</mn>
</msqrt>
<mn>3</mn>
</mroot>
<mo>+</mo>
<mn>0</mn>
</math>The <msqrt> and <mroot> elements sets math-shift to compact. The <mroot> element sets increments scriptleveldisplaystyle
mroot > :not(:first-child) {
math-depth: add(2);
math-style: compact;
}
mroot, msqrt {
math-shift: compact;
}If the <msqrt> or <mroot> element do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
If the <mroot> has less or more than two in-flow children, its layout algorithm is the same as the <mrow>
Note
In practice, an
<mroot>
element has two children that are
in-flow. Hence the CSS rules basically performs
scriptleveland
displaystylechanges for the index.
The children of the <msqrt> element are laid out using the algorithm of the <mrow>
The radical symbol must only be painted if the visibility of the <msqrt> or <mroot> element is visible. In that case, the radical symbol must be painted with the color of that element.
The radical glyph is the glyph obtained for the character U+221A SQUARE ROOT.
The radical gap is given by RadicalVerticalGap if the math-style is compact and RadicalDisplayStyleVerticalGap if the math-style is normal.
The radical target size for the stretchy radical glyph is the sum of RadicalRuleThickness, radical gap and the ink height of the base.
The box metrics of the radical glyph and painting of the surd are given by the algorithm to shape a stretchy glyph to block dimension the target size for the radical glyph.
The <msqrt> element is laid out as shown on Figure 14.
<msqrt> element
The min-content inline size (respectively max-content inline size) of the content is the sum of the preferred inline size of a glyph stretched along the block axis for the radical glyph and of the min-content inline size (respectively max-content inline size) of the msqrt base's margin box.
The inline size of the content is the sum of the advance width of the box metrics of the radical glyph and of the inline size of the msqrt base's margin's box.
The line-ascent of the content is the maximum between:
The line-descent of the content is the maximum between:
The inline size of the overbar is the inline size of the msqrt base's margin's box. The inline offsets of the msqrt base and overbar are also the same and equal to the width of the box metrics of the radical glyph.
The alphabetic baseline of the msqrt base is aligned with the alphabetic baseline. The block size of the overbar is RadicalRuleThickness. Its vertical center is shifted away from the alphabetic baseline by a distance towards the line-over equal to the line-ascent of the content, minus the RadicalExtraAscender, minus half the RadicalRuleThickness.
Finally, the painting of the surd is performed:
The <mroot> element is laid out as shown on Figure 15. The mroot index is first ignored and the mroot base and radical glyph are laid out as shown on figure Figure 14 using the same algorithm as in 3.3.3.2 Square root in order to produce a margin box B (represented in green).
<mroot> element
The min-content inline size (respectively max-content inline size) of the content is the sum of max(0, RadicalKernBeforeDegree), the mroot index's min-content inline size (respectively max-content inline size) of the mroot index's margin box, max(โmin-content inline size, RadicalKernAfterDegree) (respectively max(โmax-content inline size, RadicalKernAfterDegree)) and of the min-content inline size (respectively max-content inline size) of B.
Using the same clamping, AdjustedRadicalKernBeforeDegree and AdjustedRadicalKernAfterDegree are respectively defined as max(0, RadicalKernBeforeDegree) and is max(โinline size of the index's margin box, RadicalKernAfterDegree).
The inline size of the content is the sum of AdjustedRadicalKernBeforeDegree, the inline size of the index's margin box, AdjustedRadicalKernAfterDegree and of the inline size of B.
The line-ascent of the content is the maximum between:
The line-descent of the content is the maximum between:
The inline offset of the index is AdjustedRadicalKernBeforeDegree. The inline-offset of the mroot base is the same + the inline size of the index's margin box.
The alphabetic baseline of B is aligned with the alphabetic baseline. The alphabetic baseline of the index is shifted away from the line-under edge by a distance of RadicalDegreeBottomRaisePercent ร the block size of B + the line-descent of the index's margin box.
Note
In general, the kerning before the root index is positive while the kerning after it is negative, which means that the root element will have some inline-start space and that the root index will overlap the surd.
Historically, the <mstyle> element was introduced to make style changes that affect the rendering of its contents.
The <mstyle> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mrow>
Note
<mstyle> is implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use CSS for styling.
In the following example, <mstyle> is used to set the scriptlevel and displaystyle. Observe this is respectively affecting the font-size and placement of subscripts of their descendants. In MathML Core, one could just have used <mrow> elements instead.
<math>
<munder>
<mo movablelimits="true">*</mo>
<mi>A</mi>
</munder>
<mstyle scriptlevel="1">
<mstyle displaystyle="true">
<munder>
<mo movablelimits="true">*</mo>
<mi>B</mi>
</munder>
<munder>
<mo movablelimits="true">*</mo>
<mi>C</mi>
</munder>
</mstyle>
<munder>
<mo movablelimits="true">*</mo>
<mi>D</mi>
</munder>
</mstyle>
</math>The <merror> element displays its contents as an โerror messageโ. The intent of this element is to provide a standard way for programs that generate MathML from other input to report syntax errors in their input.
In the following example, <merror> is used to indicate a parsing error for some LaTeX-like input:
<math>
<mfrac>
<merror>
<mtext>Syntax error: \frac{1}</mtext>
</merror>
<mn>3</mn>
</mfrac>
</math>The <merror> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mrow>
merror {
border: 1px solid red;
background-color: lightYellow;
}The <mpadded> element renders the same as its in-flow child content, but with the size and relative positioning point of its content modified according to <mpadded>โs attributes.
The <mpadded> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:
The mpadded@width, mpadded@height, mpadded@depth, mpadded@lspace and mpadded@voffset if present, must have a value that is a valid length-percentage.
In the following example, <mpadded> is used to tweak spacing around a fraction (a blue background is used to visualize it). Without attributes, it behaves like an <mrow> but the attributes allow to specify the size of the box (width, height, depth) and position of the fraction within that box (lspace and voffset).
<math>
<mrow>
<mn>1</mn>
<mpadded style="background: lightblue;">
<mfrac>
<mn>23456</mn>
<mn>78</mn>
</mfrac>
</mpadded>
<mn>9</mn>
</mrow>
<mo>+</mo>
<mrow>
<mn>1</mn>
<mpadded lspace="2em" voffset="-1em" height="1em" depth="3em" width="7em"
style="background: lightblue;">
<mfrac>
<mn>23456</mn>
<mn>78</mn>
</mfrac>
</mpadded>
<mn>9</mn>
</mrow>
</math>In-flow children of the <mpadded> element are laid out using the algorithm of the <mrow><mpadded> parameters are determined as follows:
width (respectively height, depth, lspace, voffset) attribute is absent, invalid or a length-percentage then the requested width (respectively height, depth, lspace, voffset) is the inner inline size (respectively inner line-ascent, inner line-descent, 0, 0).width attribute (respectively height, depth, lspace, voffset attributes). If one of the requested width, depth, height or lspace values is negative then it is treated as 0.Note
Negative voffset values are not clamped to 0.
If the <mpadded> element does not have its computed display property equal to block math or inline math then it is laid out according to the CSS specification where the corresponding value is described. Otherwise, it is laid out as shown on Figure 16.
<mpadded> element
The min-content inline size (respectively max-content inline size) of the content is the requested width calculated in 3.3.6.1 Inner box and requested parameters but using the min-content inline size (respectively max-content inline size) of the mpadded inner box instead of the "inner inline size".
The inline size of the content is the requested width calculated in 3.3.6.1 Inner box and requested parameters.
The line-ascent of the content is the requested height. The line-descent of the content is the requested depth.
The mpadded inner box is placed so that its alphabetic baseline is shifted away from the alphabetic baseline by the requested voffset towards the line-over.
Historically, the <mphantom> element was introduced to render its content invisibly, but with the same metrics size and other dimensions, including alphabetic baseline position that its contents would have if they were rendered normally.
In the following example, <mphantom> is used to ensure alignment of corresponding parts of the numerator and denominator of a fraction:
<math>
<mfrac>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
<mo>+</mo>
<mi>z</mi>
</mrow>
<mrow>
<mi>x</mi>
<mphantom>
<mo form="infix">+</mo>
<mi>y</mi>
</mphantom>
<mo>+</mo>
<mi>z</mi>
</mrow>
</mfrac>
</math>The <mphantom> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mrow>
mphantom {
visibility: hidden;
}Note
<mphantom> is implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use CSS for styling.
The elements described in this section position one or more scripts around a base. Attaching various kinds of scripts and embellishments to symbols is a very common notational device in mathematics. For purely visual layout, a single general-purpose element could suffice for positioning scripts and embellishments in any of the traditional script locations around a given base. However, in order to capture the abstract structure of common notation better, MathML provides several more specialized scripting elements.
In addition to sub/superscript elements, MathML has overscript and underscript elements that place scripts above and below the base. These elements can be used to place limits on large operators, or for placing accents and lines above or below the base.
The <msub>, <msup> and <msubsup> elements are used to attach subscript and superscript to a MathML expression. They accept the attributes described in 2.1.3 Global Attributes.
The following example, shows basic use of subscripts and superscripts. The font-size is automatically scaled down within the scripts.
<math>
<msub>
<mn>1</mn>
<mn>2</mn>
</msub>
<mo>+</mo>
<msup>
<mn>3</mn>
<mn>4</mn>
</msup>
<mo>+</mo>
<msubsup>
<mn>5</mn>
<mn>6</mn>
<mn>7</mn>
</msubsup>
</math>If the <msub>, <msup> or <msubsup> elements do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
If the <msub> element has less or more than two in-flow children, its layout algorithm is the same as the <mrow>
If the <msup> element has less or more than two in-flow children, its layout algorithm is the same as the <mrow>
If the <msubsup> element has less or more than three in-flow children, its layout algorithm is the same as the <mrow>
The <msub> element is laid out as shown on Figure 17. LargeOpItalicCorrection is the italic correction of the msub base if it is an embellished operator with the largeop
<msub> element
The min-content inline size (respectively max-content inline size) of the content is the min-content inline size (respectively max-content inline size) inline size of the msub base's margin box โ LargeOpItalicCorrection + min-content inline size (respectively max-content inline size) of the msub subscript's margin box + SpaceAfterScript.
If there is an inline stretch size constraint or a block stretch size constraint then the msub base is also laid out with the same stretch size contraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.
The inline size of the content is the inline size of the msub base's margin box โ LargeOpItalicCorrection + the inline size of the msub subscript's margin box + SpaceAfterScript.
SubShift is the maximum between:
The line-ascent of the content is the maximum between:
SubShift.The line-descent of the content is the maximum between:
SubShift.The inline offset of the msub base is 0 and the inline offset of the msub subscript is the inline size of the msub base's margin box โ LargeOpItalicCorrection.
The msub base is placed so that its alphabetic baseline matches the alphabetic baseline. The msub subscript is placed so that its alphabetic baseline is shifted away from the alphabetic baseline by SubShift towards the line-under.
The <msup> element is laid out as shown on Figure 18. ItalicCorrection is the italic correction of the msup base if it is not an embellished operator with the largeop
<msup> element
The min-content inline size (respectively max-content inline size) of the content is the min-content inline size (respectively max-content inline size) of the msup base's margin box + ItalicCorrection + the min-content inline size (respectively max-content inline size) of the msup superscript's margin box + SpaceAfterScript.
If there is an inline stretch size constraint or a block stretch size constraint then the msup base is also laid out with the same stretch size contraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.
The inline size of the content is the inline size of the msup base's margin box + ItalicCorrection + the inline size of the msup superscript's margin box + SpaceAfterScript.
SuperShift is the maximum between:
math-shift property equal to compact, or SuperscriptShiftUp otherwise.The line-ascent of the content is the maximum between:
SuperShift.The line-descent of the content is the maximum between:
SuperShift.The inline offset of the msup base is 0 and the inline offset of msup superscript is the inline size of the msup base's margin box + ItalicCorrection.
The msup base is placed so that its alphabetic baseline matches the alphabetic baseline. The msup superscript is placed so that its alphabetic baseline is shifted away from the alphabetic baseline by SuperShift towards the line-over.
The <msubsup> element is laid out as shown on Figure 18. LargeOpItalicCorrection and SubShift are set as in 3.4.1.2 Base with subscript. ItalicCorrection and SuperShift are set as in 3.4.1.3 Base with superscript.
<msubsup> element
The min-content inline size (respectively max-content inline size and inline size) of the content is the maximum between the min-content inline size (respectively max-content inline size and inline size) of the content calculated in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript.
If there is an inline stretch size constraint or a block stretch size constraint then the msubsup base is also laid out with the same stretch size contraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.
If there is an inline stretch size constraint or a block stretch size constraint then the msubsup base is also laid out with the same stretch size contraint and otherwise it is laid out without any stretch size constraint. The scripts are always laid out without any stretch size constraint.
SubSuperGap is the gap between the two scripts along the block axis and is defined by (SubShift โ the ink line-ascent of the msubsup subscript's margin box) + (SuperShift โ the ink line-descent of the msubsup superscript's margin box). If SubSuperGap is not at least SubSuperscriptGapMin then the following steps are performed to ensure that the condition holds:
SuperShift โ the ink line-descent of the msubsup superscript's margin box). If ฮ > 0 then set ฮ to the minimum between ฮ set SubSuperscriptGapMin โ SubSuperGap and increase SuperShift (and so SubSuperGap too) by ฮ.SubSuperGap. If ฮ > 0 then increase SubscriptShift (and so SubSuperGap too) by ฮ.The ink line-ascent (respectively line-ascent, ink line-descent, line-descent) of the content is set to the maximum of the ink line-ascent (respectively line-ascent, ink line-descent, line-descent) of the content calculated in in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript but using the adjusted values SubShift and SuperShift above.
The inline offset and block offset of the msubsup base and scripts are performed the same as described in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript.
The <munder>, <mover> and <munderover> elements are used to attach accents or limits placed under or over a MathML expression.
The <munderover> element accepts the attribute described in 2.1.3 Global Attributes as well as the following attributes:
Similarly, the <mover> element (respectively <munder> element) accepts the attribute described in 2.1.3 Global Attributes as well as the accentaccentunder
accent, accentunder, attributes, if present, must have values that are booleans. If these attributes are absent or invalid, they are treated as equal to false. User agents must implement them as described in 3.4.4 Displaystyle, scriptlevel and math-shift in scripts.
The following example, shows basic use of under and over scripts. The font-size is automatically scaled down within the scripts, unless they are meant to be accents.
<math>
<munder>
<mn>1</mn>
<mn>2</mn>
</munder>
<mo>+</mo>
<mover>
<mn>3</mn>
<mn>4</mn>
</mover>
<mo>+</mo>
<munderover>
<mn>5</mn>
<mn>6</mn>
<mn>7</mn>
</munderover>
<mo>+</mo>
<munderover accent="true">
<mn>8</mn>
<mn>9</mn>
<mn>10</mn>
</munderover>
<mo>+</mo>
<munderover accentunder="true">
<mn>11</mn>
<mn>12</mn>
<mn>13</mn>
</munderover>
</math>If the <munder>, <mover> or <munderover> elements do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
If the <munder> element has less or more than two in-flow children, its layout algorithm is the same as the <mrow>
If the <mover> element has less or more than two in-flow children, its layout algorithm is the same as the <mrow>
If the <munderover> element has less or more than three in-flow children, its layout algorithm is the same as the <mrow>
If the <munder>, <mover> or <munderover> elements have a computed math-style property equal to compact and their base is an embellished operator with the movablelimits<msub>, <msup> and <msubsup> in 3.4.1.2 Base with subscript, 3.4.1.3 Base with superscript and 3.4.1.4 Base with subscript and superscript.
Otherwise, the <mover>, <mover> and <munderover> layout algorithms are respectively described in 3.4.2.3 Base with underscript, 3.4.2.4 Base with overscript and 3.4.2.5 Base with underscript and overscript
The algorithm for stretching operators along the inline axis is as follows.
LToStretch containing embellished operators with a stretchy property and inline stretch axis ; and a second list LNotToStretch.LNotToStretch. If LToStretch is empty then stop. If LNotToStretch is empty, perform layout with stretch size constraint 0 on all the items of LToStretch.T to the maximum inline size of the margin boxes of child boxes that have been laid out in the previous step.LToStretch with inline stretch size constraint T.The <munder> element is laid out as shown on Figure 20. LargeOpItalicCorrection is the italic correction of the munder base if it is an embellished operator with the largeop
<munder> element
The min-content inline size (respectively max-content inline size) of the content are calculated like the inline size of the content below but replacing the inline sizes of the munder base's margin box and munder underscript's margin box with the min-content inline size (respectively max-content inline size) of the munder base's margin box and munder underscript's margin box.
The in-flow children are laid out using the algorithm for stretching operators along the inline axis.
The inline size of the content is calculated by determining the absolute difference between:
LargeOpItalicCorrection.LargeOpItalicCorrection.If m is the minimum calculated in the second item above then the inline offset of the munder base is โm โ half the inline size of the base's margin box. The inline offset of the munder underscript is โm โ half the inline size of the munder underscript's margin box โ half LargeOpItalicCorrection.
Parameters UnderShift and UnderExtraDescender are determined by considering three cases in the following order:
The munder base is an embellished operator with the largeopUnderShift is the maximum of
UnderExtraDescender is 0.
The munder base is an embellished operator with the stretchyUnderShift is the maximum of:
UnderExtraDescender is 0.UnderShift is equal to UnderbarVerticalGap if the accentunder attribute is not an ASCII case-insensitive match to true and to zero otherwise. UnderExtraAscender is UnderbarExtraDescender.The line-ascent of the content is the maximum between:
UnderShift.The line-descent of the content is the maximum between:
UnderShift + UnderExtraAscender.The alphabetic baseline of the munder base is aligned with the alphabetic baseline. The alphabetic baseline of the munder underscript is shifted away from the alphabetic baseline and towards the line-under by a distance equal to the ink line-descent of the munder base's margin box + UnderShift.
The <mover> element is laid out as shown on Figure 21. LargeOpItalicCorrection is the italic correction of the mover base if it is an embellished operator with the largeop
<mover> element
The min-content inline size (respectively max-content inline size) of the content are calculated like the inline size of the content below but replacing the inline sizes of the mover base's margin box and mover overscript's margin box with the min-content inline size (respectively max-content inline size) of the mover base's margin box and mover overscript's margin box.
The in-flow children are laid out using the algorithm for stretching operators along the inline axis.
The TopAccentAttachment is the top accent attachment of the mover overscript or half the inline size of the mover overscript's margin box if it is undefined.
The inline size of the content is calculated by applying the algorithm for stretching operators along the inline axis for layout and determining the absolute difference between:
TopAccentAttachment + half LargeOpItalicCorrection.TopAccentAttachment + half LargeOpItalicCorrection.If m is the minimum calculated in the second item above then the inline offset of the mover base is โm โ half the inline size of the base's margin. The inline offset of the mover overscript is โm โ half the inline size of the mover overscript's margin box + half LargeOpItalicCorrection.
Parameters OverShift and OverExtraDescender are determined by considering three cases in the following order:
The mover base is an embellished operator with the largeopOverShift is the maximum of
OverExtraAscender is 0.
The mover base is an embellished operator with the stretchyOverShift is the maximum of:
OverExtraDescender is 0.Otherwise, OverShift is equal to
accent attribute is not an ASCII case-insensitive match to true.OverExtraAscender is OverbarExtraAscender.
Note
For accent overscripts and bases with
line-ascentsthat are at most
AccentBaseHeight, the rule from [
OPEN-FONT-FORMAT] [
TEXBOOK] is actually to align the
alphabetic baselinesof the overscripts and of the bases. This assumes that accent glyphs are designed in such a way that their ink bottoms are more or less
AccentBaseHeightabove their
alphabetic baselines. Hence, the previous rule will guarantee that all the overscript bottoms are aligned while still avoiding collision with the bases. However, MathML can have arbitrary accent overscripts a more general and simpler rule is provided above: Ensure that the bottom of overscript is at least
AccentBaseHeightabove the
alphabetic baselineof the base.
The line-ascent of the content is the maximum between:
OverShift + OverExtraAscender.The line-descent of the content is the maximum between:
OverShift.The alphabetic baseline of the mover base is aligned with the alphabetic baseline. The alphabetic baseline of the mover overscript is shifted away from the alphabetic baseline and towards the line-over by a distance equal to the ink line-ascent of the base + OverShift.
The general layout of <munderover> is shown on Figure 22. The LargeOpItalicCorrection, UnderShift, UnderExtraDescender, OverShift, OverExtraDescender parameters are calculated the same as in 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript.
<munderover> element
The min-content inline size, max-content inline size and inline size of the content are calculated as an absolute difference between a maximum inline offset and minimum inline offset. These extrema are calculated by taking the extremum value of the corresponding extrema calculated in 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript. The inline offsets of the munderover base, munderover underscript and munderover overscript are calculated as in these sections but using the new minimum m (minimum of the corresponding minima).
Like in these sections, the in-flow children are laid out using the algorithm for stretching operators along the inline axis.
The line-ascent and line-descent of the content are also calculated by taking the extremum value of the extrema calculated in 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript.
Finally, the alphabetic baselines of the munderover base, munderover underscript and munderover overscript are calculated as in sections 3.4.2.3 Base with underscript and 3.4.2.4 Base with overscript.
Note
When the underscript (respectively overscript) is an empty box, the base and overscript (respectively underscript) are laid out similarly to 3.4.2.4 Base with overscript (respectively 3.4.2.3 Base with underscript) but the position of the empty underscript (respectively overscript) may add extra space. In order to keep the algorithm simple, no attempt is made to handle empty scripts in a special way.
Presubscripts and tensor notations are represented the <mmultiscripts> with hints given by the <mprescripts> (to distinguish postscripts and prescripts) and <none> elements (to indicate empty scripts). These element accept the attributes described in 2.1.3 Global Attributes.
The following example, shows basic use of prescripts and postscripts, involving <none> and <mprescripts>. The font-size is automatically scaled down within the scripts.
<math>
<mmultiscripts>
<mn>1</mn>
<mn>2</mn>
<mn>3</mn>
<none/>
<mn>5</mn>
<mprescripts/>
<mn>6</mn>
<none/>
<mn>8</mn>
<mn>9</mn>
</mmultiscripts>
</math>If the <mmultiscripts>, <mprescripts> or <none> elements do not have their computed display property equal to block math or inline math then they are laid out according to the CSS specification where the corresponding value is described. Otherwise, the layout below is performed.
The empty <mprescripts> and <none> elements are laid out as an <mrow>
A valid <mmultiscripts> element contains the following in-flow children:
<mprescripts><mprescripts><mprescripts><mprescripts>If an <mmultiscripts> element is not valid then it is laid out the same as the <mrow>
Note
The <none> element is preserved for backward compatibility reasons but is actually not taken into account in the layout algorithm.
The <mmultiscripts> element is laid out as shown on Figure 23. For each subscript/superscript pair of mmultiscripts postscripts, the ItalicCorrection LargeOpItalicCorrection are defined as in 3.4.1.2 Base with subscript and 3.4.1.3 Base with superscript.
<mmultiscripts> element
The min-content inline size (respectively max-content inline size) of the content is calculated the same as the inline size of the content below, but replacing "inline size" with "min-content inline size" (respectively "max-content inline size") for the mmultiscripts base's margin box and scripts's margin boxes.
If there is an inline stretch size constraint or a block stretch size constraint the mmultiscripts base is also laid out with the same stretch size constraint. Otherwise it is laid out without any stretch size constraint. The other elements are always laid out without any stretch size constraint.
The inline size of the content is calculated with the following algorithm:
inline-offset to 0.For each subscript/superscript pair of mmultiscripts prescripts, increment inline-offset by SpaceAfterScript + the maximum of
inline-offset by the inline size of the mmultiscripts base's margin box and set inline-size to inline-offset.For each subscript/superscript pair of mmultiscripts postscripts, modify inline-size to be at least:
LargeOpItalicCorrection.ItalicCorrection.Increment inline-offset to the maximum of:
Increment inline-offset by SpaceAfterScript.
inline-sizeSubShift (respectively SuperShift) is calculated by taking the maximum of all subshifts (respectively supershifts) of each subscript/superscript pair as described in 3.4.1.4 Base with subscript and superscript.
The line-ascent of the content is calculated by taking the maximum of all the line-ascent of each subscript/superscript pair as described in 3.4.1.4 Base with subscript and superscript but using the SubShift and SuperShift values calculated above.
The line-descent of the content is calculated by taking the maximum of all the line-descent of each subscript/superscript pair as described in 3.4.1.4 Base with subscript and superscript but using the SubShift and SuperShift values calculated above.
Finally, the placement of the in-flow children is performed using the following algorithm:
inline-offset to 0.For each subscript/superscript pair of mmultiscripts prescripts:
inline-offset by SpaceAfterScript.pair-inline-size to the maximum of
inline-offset + pair-inline-size โ the inline size of the subscript's margin box.inline-offset + pair-inline-size โ the inline size of the superscript's margin box.SubShift (respectively SuperShift) towards the line-under (respectively line-over).inline-offset by pair-inline-size.<mprescripts> boxes at inline offsets inline-offset and with their alphabetic baselines aligned with the alphabetic baseline.For each subscript/superscript pair of mmultiscripts postscripts:
pair-inline-size to the maximum of
inline-offset โ LargeOpItalicCorrection.inline-offset + ItalicCorrection.SubShift (respectively SuperShift) towards the line-under (respectively line-over).inline-offset by pair-inline-sizeinline-offset by SpaceAfterScript.Note
An <mmultiscripts> with only one subscript/superscript pair of mmultiscripts postscripts is laid out the same as a <msubsup> with the same in-flow children. However, as noticed for <msubsup>, if additionally the subscript (respectively superscript) is an empty box then it is not necessarily laid out the same as an <msub> (respectively <msup>) element. In order to keep the algorithm simple, no attempt is made to handle empty or <none> scripts in a special way.
For all scripted elements, the rule of thumb is to set displaystylefalse and to increment scriptlevel<mover><munderover>accenttrue does not increment scriptlevel within its second child (respectively third child). Similarly, <mover><munderover>accentundertrue do not increment scriptlevel within their second child.
<mmultiscripts> sets math-shiftcompact on its children at even position if they are before an <mprescripts>, and on those at odd position if they are after an <mprescripts>. The <msub> and <msubsup> elements set math-shiftcompact on their second child. An <mover><munderover>accenttrue also sets math-shiftcompact within their first child.
The A. User Agent Stylesheet must contain the following style in order to implement this behavior:
msub > :not(:first-child),
msup > :not(:first-child),
msubsup > :not(:first-child),
mmultiscripts > :not(:first-child),
munder > :not(:first-child),
mover > :not(:first-child),
munderover > :not(:first-child) {
math-depth: add(1);
math-style: compact;
}
munder[accentunder="true" i] > :nth-child(2),
mover[accent="true" i] > :nth-child(2),
munderover[accentunder="true" i] > :nth-child(2),
munderover[accent="true" i] > :nth-child(3) {
font-size: inherit;
}
msub > :nth-child(2),
msubsup > :nth-child(2),
mmultiscripts > :nth-child(even),
mmultiscripts > mprescripts ~ :nth-child(odd),
mover[accent="true" i] > :first-child,
munderover[accent="true" i] > :first-child {
math-shift: compact;
}
mmultiscripts > mprescripts ~ :nth-child(even) {
math-shift: inherit;
}Note
In practice, all the children of the MathML elements described in this section are
in-flowand the
<mprescripts>
is empty. Hence the CSS rules essentially performs automatic
displaystyleand
scriptlevelchanges for the scripts ; and
math-shiftchanges for subscripts and sometimes the base.
Matrices, arrays and other table-like mathematical notation are marked up using <mtable><mtr><mtd><table>, <tr> and <td> elements of [HTML].
The following example, how tabular layout allows to write a matrix. Note that it is vertically centered with the fraction bar and the middle of the equal sign.
<math>
<mfrac>
<mi>A</mi>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable>
<mtr>
<mtd><mn>1</mn></mtd>
<mtd><mn>2</mn></mtd>
<mtd><mn>3</mn></mtd>
</mtr>
<mtr>
<mtd><mn>4</mn></mtd>
<mtd><mn>5</mn></mtd>
<mtd><mn>6</mn></mtd>
</mtr>
<mtr>
<mtd><mn>7</mn></mtd>
<mtd><mn>8</mn></mtd>
<mtd><mn>9</mn></mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math>The <mtable> is laid out as an inline-table and sets displaystyle to false. The user agent stylesheet must contain the following rules in order to implement these properties:
mtable {
display: inline-table;
math-style: compact;
}The mtable element is as a CSS table and the min-content inline size, max-content inline size, inline size, block size, first baseline set and last baseline set sets are determined accordingly. The center of the table is aligned with the math axis.
The <mtr> is laid out as table-row. The user agent stylesheet must contain the following rules in order to implement that behavior:
mtr {
display: table-row;
}The <mtr> accepts the attributes described in 2.1.3 Global Attributes.
The <mtd> is laid out as a table-cell with content centered in the cell and a default padding. The user agent stylesheet must contain the following rules:
mtd {
display: table-cell;
text-align: center;
padding: 0.5ex 0.4em;
}The <mtd> accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:
The columnspan (respectively rowspan) attribute has the same syntax and semantic as the colspan (respectively rowspan) attribute on the <td> element from [HTML].
Note
The name for the column spanning attribute is
columnspan
as in [
MathML3] and not
colspan
as in [
HTML].
Historically, the <maction> element provides a mechanism for binding actions to expressions.
The <maction> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attributes:
This specification does not define any observable behavior that is specific to the actiontype and selection attributes.
The following example, shows the "toggle" action type from [MathML3] where the renderer alternately displays the selected subexpression, starting from "one third" and cycling through them when there is a click on the selected subexpression ("one quarter", "one half", "one third", etc). This is not part of MathML Core but can be implemented using JavaScript and CSS polyfills. The default behavior is just to render the first child.
<math>
<maction actiontype="toggle" selection="2">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</maction>
</math>The layout algorithm of the <maction> element the same as the <mrow> element. The user agent stylesheet must contain the following rules in order to hide all but its first child element, which is the default behavior for the legacy actiontype values:
maction > :not(:first-child) {
display: none;
}Note
<maction>
is implemented for compatibility with full MathML. Authors whose only target is MathML Core are encouraged to use other HTML, CSS and JavaScript mechanisms to implement custom actions. They may rely on maction attributes defined in [
MathML3].
The <semantics> element is the container element that associates annotations with a MathML expression. Typically, the <semantics> element has as its first child element a MathML expression to be annotated while subsequent child elements represent text annotations within an <annotation> element, or more complex markup annotations within an <annotation-xml> element.
The following example, shows how the fraction "one half" can be annotated with a textual annotation (LaTeX) or an XML annotation (content MathML). These annotations are not intended to be rendered by the user agent.
<math>
<semantics>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<annotation encoding="application/x-tex">\frac{1}{2}</annotation>
<annotation-xml encoding="application/mathml-content+xml">
<apply>
<divide/>
<cn>1</cn>
<cn>2</cn>
</apply>
</annotation-xml>
</semantics>
</math>The <semantics> element accepts the attributes described in 2.1.3 Global Attributes. Its layout algorithm is the same as the <mrow>
semantics > :not(:first-child) {
display: none;
}The <annotation-xml> and <annotation> element accepts the attributes described in 2.1.3 Global Attributes as well as the following attribute:
This specification does not define any observable behavior that is specific to the encoding attribute.
The layout algorithm of the <annotation-xml> and <annotation> element is the same as the <mtext>
Note
Authors can use the
encodingattribute to distinguish annotations for
HTML integration point, clipboard copy, alternative rendering, etc. In particular, CSS can be used to render alternative annotations e.g.
semantics > :first-child { display: none; }
semantics > annotation { display: inline; }
semantics > annotation-xml[encoding="text/html" i],
semantics > annotation-xml[encoding="application/xhtml+xml" i] {
display: inline-block;
}The display property from CSS Display Module Level 3 is extended with a new inner display type:
<display> = <display-inside-old> | math
For elements that are not MathML elements, if the specified value of display is inline math or block math then the computed value is block flow and inline flow respectively. For the <mtable>block table and inline table respectively. For the <mtr>table-row. For the <mtd>table-cell.
MathML elements with a computed display value equal to block math or inline math control box generation and layout according to their tag name, as described in the relevant sections. Unknown MathML elements behave the same as the <mrow>
Note
The
display: block math
and
display: inline math
values provide a default layout for MathML elements while at the same time allowing to override it with either native display values or
custom values. This allows authors or polyfills to define their own custom notations to tweak or extend MathML Core.
In the following example, the default layout of the MathML <mrow> element is overriden to render its content as a grid.
<math>
<msup>
<mrow>
<mo symmetric="false">[</mo>
<mrow style="display: block; width: 4.5em;">
<mrow style="display: grid;
grid-template-columns: 1.5em 1.5em 1.5em;
grid-template-rows: 1.5em 1.5em;
justify-items: center;
align-items: center;">
<mn>12</mn>
<mn>34</mn>
<mn>56</mn>
<mn>7</mn>
<mn>8</mn>
<mn>9</mn>
</mrow>
</mrow>
<mo symmetric="false">]</mo>
</mrow>
<mi>ฮฑ</mi>
</msup>
</math>The text-transform property from CSS Text Module Level 3 is extended with new values:
<text-transform> = <text-transform-old> | math-auto | math-bold | math-italic | math-bold-italic | math-double-struck | math-bold-fraktur | math-script | math-bold-script | math-fraktur | math-sans-serif | math-bold-sans-serif | math-sans-serif-italic | math-sans-serif-bold-italic | math-monospace | math-initial | math-tailed | math-looped | math-stretched
If the specified value of text-transform is math-auto and the inherited value is not none then the computed value is the inherited value.
On text nodes containing a unique character, math-auto has the same effect as math-italic, otherwise it has no effects.
For the math-bold, math-italic, math-bold-italic, math-double-struck, math-bold-fraktur, math-script, math-bold-script, math-fraktur, math-sans-serif, math-bold-sans-serif, math-sans-serif-italic, math-sans-serif-bold-italic, math-monospace, math-initial, math-tailed, math-looped and math-stretched values, the transformed text is obtained by performing conversion of each character according to the corresponding bold, italic, bold-italic, double-struck, bold-fraktur, script, bold-script, fraktur, sans-serif, bold-sans-serif, sans-serif-italic, sans-serif-bold-italic, monospace, initial, tailed, looped, stretched tables.
User agents may decide to rely on italic, bold and bold-italic font-level properties when available fonts lack the proper glyphs to perform math-auto, math-italic, math-bold, math-bold-italic character-level transforms.
The following example shows a mathematical formula where "exp" is rendered with normal variant, "A" with bold variant, "gl" with fraktur variant, "n" using italic variant and and "R" using double-struck variant.
Values other than math-auto are intended to infer specific context-dependent mathematical meaning. In the previous example, one can guess that the author decided to use the convention of bold variables for matrices, fraktur variables for Lie algebras and double-struck variables for set of numbers. Although the corresponding Unicode characters could have been used directly in these cases, it may be helpful for authoring tools or polyfills to support these transformations via the text-transform property.
A common style convention is to render identifiers with multiple letters (e.g. the function name "exp") with normal style and identifiers with a single letter (e.g. the variable "n") with italic style. The math-auto property is intended to implement this default behavior, which can be overriden by authors if necessary. Note that mathematical fonts are designed with special kind of italic glyphs located at the Unicode positions of C.13 italic mappings, which differ from the shaping obtained via italic font style. Compare this mathematical formula rendered with the Latin Modern Math font using font-style: italic (left) and text-transform: math-auto (right):
math-style Value: normal | compact Initial: normal Applies to: All elements Inherited: yes Percentages: n/a Media: visual Computed value: specified keyword Canonical order: n/a Animation type: not animatable
When math-style is compact, the math layout on descendants try to minimize the logical height by applying the following rules:
font-size is scaled down when its specified value is math and the computed value of math-depthauto-add (default for <mfrac>) as described in 4.5 New value math-depth property.largeop property do not follow rules from 3.2.4.3 Layout of operators to make them bigger.movablelimits property are actually drawn as sub/super scripts as described in 3.4.2.1 Children of <munder>, <mover>, <munderover>.The following example shows a mathematical formula renderered with its <math>math-style: compact (left) and math-style: normal (right). In the former case, the font-size is automatically scaled down within the fractions and the summation limits are rendered as subscript and superscript of the โ. In the latter case, the โ is drawn bigger than normal text and vertical gaps within fractions (even relative to current font-size) is larger.
These two math-style values typically correspond to mathematical expressions in inline and display mode respectively [TeXBook]. A mathematical formula in display mode may automatically switch to inline mode within some subformulas (e.g. scripts, matrix elements, numerators and denominators, etc) and it is sometimes desirable to override this default behavior. The math-style property allows to easily implement these features for MathML in the User Agent Stylesheet and with the displaystyle attribute ; and also exposes them to polyfills.
math-shift Value: normal | compact Initial: normal Applies to: All elements Inherited: yes Percentages: n/a Media: visual Computed value: specified keyword Canonical order: n/a Animation type: not animatable
If the value of math-shift is compact, the math layout on descendants will use the superscriptShiftUpCramped parameter to place superscript. If the value of math-shift is normal, the math will use the superscriptShiftUp parameter instead.
This property is used for positioning superscript during the layout of MathML scripted elements. See ยง 3.4.1 Subscripts and Superscripts <msub>, <msup>, <msubsup> 3.4.3 Prescripts and Tensor Indices <mmultiscripts> and 3.4.2 Underscripts and Overscripts <munder>, <mover>, <munderover>.
In the following example, the two "x squared" are rendered with compact math-style and the same font-size. However, the one within the square root is rendered with compact math-shift while the other one is rendered with normal math-shift, leading to subtle different shift of the superscript "2".
Per [TeXBook], a mathematical formula uses normal style by default but may switch to compact style ("cramped" in TeX's terminology) within some subformulas (e.g. radicals, fraction denominators, etc). The math-shift property allows to easily implement these rules for MathML in the User Agent Stylesheet. Page authors or developers of polyfills may also benefit from having access to this property to tweak or refine the default implementation.
A new math-depth property is introduced to describe a notion of "depth" for each element of a mathematical formula, with respect to the top-level container of that formula. Concretely, this is used to determine the computed value of the font-size property when its specified value is math.
math-depth Value: auto-add | add(<integer>) | <integer> Initial: 0 Applies to: All elements Inherited: yes Percentages: n/a Media: visual Computed value: an integer, see below Canonical order: n/a Animation type: not animatable
The computed value of the math-depth value is determined as follows:
math-depth is auto-add and the inherited value of math-style is compact then the computed value of math-depth of the element is its inherited value plus one.math-depth is of the form add(<integer>) then the computed value of math-depth of the element is its inherited value plus the specified integer.math-depth is of the form <integer> then the computed value of math-depth of the element is the specified integer.math-depth of the element is the inherited one.If the specified value font-size is math then the computed value of font-size is obtained by multiplying the inherited value of font-size by a nonzero scale factor calculated by the following procedure:
math-depth value, B the computed math-depth value, C be 0.71 and S be 1.0InvertScaleFactor to true.InvertScaleFactor to false.InvertScaleFactor is false and 1/S otherwise.The following example shows a mathematical formula with normal math-style rendered with the Latin Modern Math font. When entering subexpressions like scripts or fractions, the font-size is automatically scaled down according to the values of MATH table contained in that font. Note that font-size is scaled down when entering the superscripts but even faster when entering a root's prescript. Also it is scaled down when entering the inner fraction but not when entering the outer one, due to automatic change of math-style in fractions.
These rules from [TeXBook] are subtle and it's worth having a separate math-depth mechanism to express and handle them. They can be implemented in MathML using the User Agent Stylesheet. Page authors or developers of polyfills may also benefit from having access to this property to tweak or refine the default implementation. In particular, the scriptlevel attribute from MathML provides a way to perform math-depth changes.
This chapter describes features provided by MATH table of an OpenType font [OPEN-FONT-FORMAT]. Throughout this chapter, a C-like notation Table.Subtable1[index].Subtable2.Parameter is used to denote OpenType parameters. Such parameters may not be available (e.g. if the font lack one of the subtable, has an invalid offset, etc) and so fallback options are provided.
Note
It is strongly encouraged to render MathML with a math font with the proper OpenType features. There is no guarantee that the fallback options provided will provide good enough rendering.
OpenType values expressed in design units (perhaps indirectly via a MathValueRecord entry) are scaled to appropriate values for layout purpose, taking into account head.unitsPerEm, CSS font-size or zoom level.
These are global layout constants for the first available font:
post.underlineThickness or Default fallback constant if the constant is not available.
MATH.MathConstants.scriptPercentScaleDown / 100 or 0.71 if MATH.MathConstants.scriptPercentScaleDown is null or not available.
MATH.MathConstants.scriptScriptPercentScaleDown / 100 or 0.5041 if MATH.MathConstants.scriptScriptPercentScaleDown is null or not available.
MATH.MathConstants.displayOperatorMinHeight or Default fallback constant if the constant is not available.
MATH.MathConstants.axisHeight or half OS/2.sxHeight if the constant is not available.
MATH.MathConstants.accentBaseHeight or OS/2.sxHeight if the constant is not available.
MATH.MathConstants.subscriptShiftDown or OS/2.ySubscriptYOffset if the constant is not available.
MATH.MathConstants.subscriptTopMax or โ
ร OS/2.sxHeight if the constant is not available.
MATH.MathConstants.subscriptBaselineDropMin or Default fallback constant if the constant is not available.
MATH.MathConstants.superscriptShiftUp or OS/2.ySuperscriptYOffset if the constant is not available.
MATH.MathConstants.superscriptShiftUpCramped or Default fallback constant if the constant is not available.
MATH.MathConstants.superscriptBottomMin or ยผ ร OS/2.sxHeight if the constant is not available.
MATH.MathConstants.superscriptBaselineDropMax or Default fallback constant if the constant is not available.
MATH.MathConstants.subSuperscriptGapMin or 4 ร default rule thickness if the constant is not available.
MATH.MathConstants.superscriptBottomMaxWithSubscript or โ
ร OS/2.sxHeight if the constant is not available.
MATH.MathConstants.spaceAfterScript or 1/24em if the constant is not available.
MATH.MathConstants.upperLimitGapMin or Default fallback constant if the constant is not available.
MATH.MathConstants.upperLimitBaselineRiseMin or Default fallback constant if the constant is not available.
MATH.MathConstants.lowerLimitGapMin or Default fallback constant if the constant is not available.
MATH.MathConstants.lowerLimitBaselineDropMin or Default fallback constant if the constant is not available.
MATH.MathConstants.stackTopShiftUp or Default fallback constant if the constant is not available.
MATH.MathConstants.stackTopDisplayStyleShiftUp or Default fallback constant if the constant is not available.
MATH.MathConstants.stackBottomShiftDown or Default fallback constant if the constant is not available.
MATH.MathConstants.stackBottomDisplayStyleShiftDown or Default fallback constant if the constant is not available.
MATH.MathConstants.stackGapMin or 3 ร default rule thickness if the constant is not available.
MATH.MathConstants.stackDisplayStyleGapMin or 7 ร default rule thickness if the constant is not available.
MATH.MathConstants.stretchStackTopShiftUp or Default fallback constant if the constant is not available.
MATH.MathConstants.stretchStackBottomShiftDown or Default fallback constant if the constant is not available.
MATH.MathConstants.stretchStackGapAboveMin or Default fallback constant if the constant is not available.
MATH.MathConstants.stretchStackGapBelowMin or Default fallback constant if the constant is not available.
MATH.MathConstants.fractionNumeratorShiftUp or Default fallback constant if the constant is not available.
MATH.MathConstants.fractionNumeratorDisplayStyleShiftUp or Default fallback constant if the constant is not available.
MATH.MathConstants.fractionDenominatorShiftDown or Default fallback constant if the constant is not available.
MATH.MathConstants.fractionDenominatorDisplayStyleShiftDown or Default fallback constant if the constant is not available.
MATH.MathConstants.fractionNumeratorGapMin or default rule thickness if the constant is not available.
MATH.MathConstants.fractionNumDisplayStyleGapMin or 3 ร default rule thickness if the constant is not available.
MATH.MathConstants.fractionRuleThickness or default rule thickness if the constant is not available.
MATH.MathConstants.fractionDenominatorGapMin or default rule thickness if the constant is not available.
MATH.MathConstants.fractionDenomDisplayStyleGapMin or 3 ร default rule thickness if the constant is not available.
MATH.MathConstants.overbarVerticalGap or 3 ร default rule thickness if the constant is not available.
MATH.MathConstants.overbarExtraAscender or default rule thickness if the constant is not available.
MATH.MathConstants.underbarVerticalGap or 3 ร default rule thickness if the constant is not available.
MATH.MathConstants.underbarExtraDescender or default rule thickness if the constant is not available.
MATH.MathConstants.radicalVerticalGap or 1ยผ ร default rule thickness if the constant is not available.
MATH.MathConstants.radicalDisplayStyleVerticalGap or default rule thickness + ยผ OS/2.sxHeight if the constant is not available.
MATH.MathConstants.radicalRuleThickness or default rule thickness if the constant is not available.
MATH.MathConstants.radicalExtraAscender or default rule thickness if the constant is not available.
MATH.MathConstants.radicalKernBeforeDegree or 5/18em if the constant is not available.
MATH.MathConstants.radicalKernAfterDegree or โ10/18em if the constant is not available.
MATH.MathConstants.radicalDegreeBottomRaisePercent / 100.0 or 0.6 if the constant is not available.
Note
MathTopAccentAttachment is at risk.
These are per-glyph tables for the first available font:
MATH.MathGlyphInfo.MathItalicsCorrectionInfo of italics correction values. Use the corresponding value in MATH.MathGlyphInfo.MathItalicsCorrectionInfo.italicsCorrection if there is one for the requested glyph or or 0 otherwise.
MATH.MathGlyphInfo.MathTopAccentAttachment of positioning top math accents along the inline axis. Use the corresponding value in MATH.MathGlyphInfo.MathTopAccentAttachment.topAccentAttachment if there is one for the requested glyph or or half the advance width of the glyph otherwise.
This section describes how to handle stretchy glyphs of arbitrary size using the MATH.MathVariants table.
This section is based on [OPEN-TYPE-MATH-IN-HARFBUZZ]. For convenience, the following definitions are used:
MATH.MathVariant.minConnectorOverlap.GlyphPartRecord is an extender if and only if GlyphPartRecord.partFlags has the fExtender flag set.GlyphAssembly is horizontal if it is obtained from MathVariant.horizGlyphConstructionOffsets. Otherwise it is vertical (and obtained from MathVariant.vertGlyphConstructionOffsets).GlyphAssembly table, NExt (respectively NNonExt) is the number of extenders (respectively non-extenders) in GlyphAssembly.partRecords.GlyphAssembly table, SExt (respectively SNonExt) is the sum of GlyphPartRecord.fullAdvance for all extenders (respectively non-extenders) in GlyphAssembly.partRecords.User agents must treat the GlyphAssembly as invalid if the following conditions are not satisfied:
GlyphPartRecord in GlyphAssembly.partRecords, the values of GlyphPartRecord.startConnectorLength and GlyphPartRecord.endConnectorLength must be at least omin. Otherwise, it is not possible to satisfy the condition of MathVariant.minConnectorOverlap.In this specification, a glyph assembly is built by repeating each extender r times and using the same overlap value o between each glyph. The number of glyphs in such an assembly is AssemblyGlyphCount(r) = NNonExt + r NExt while the stretch size is AssembySize(o, r) = SNonExt + r SExt โ o (AssemblyGlyphCount(r) โ 1).
rmin is the minimal number of repetitions needed to obtain an assembly of size at least T i.e. the minimal r such that AssembySize(omin, r)) โฅ T. It is defined as the maximum between 0 and the ceiling of ((T โ SNonExt + omin (NNonExt โ 1)) / SExt,NonOverlapping).
omax,theorical = (AssembySize(0, rmin) โ T) / (AssemblyGlyphCount(rmin) โ 1) is the theorical overlap obtained by splitting evenly the extra size of an assembly built with null overlap.
omax is the maximum overlap possible to build an assembly of size at least T by repeating each extender rmin times. If AssemblyGlyphCount(rmin) โค 1, then the actual overlap value is irrelevant. Otherwise, omax is defined to be the minimum of:
GlyphPartRecord.startConnectorLength for all the entries in GlyphAssembly.partRecords, excluding the last one if it is not an extender.GlyphPartRecord.endConnectorLength for all the entries in GlyphAssembly.partRecords, excluding the first one if it is not an extender.The glyph assembly stretch size for a target size T is AssembySize(omax, rmin).
The glyph assembly width, glyph assembly ascent and glyph assembly descent are defined as follows:
GlyphAssembly is vertical, the width is the maximum advance width of the glyphs of id GlyphPartRecord.glyphID for all the GlyphPartRecord in GlyphAssembly.partRecords, the ascent is the glyph assembly stretch size for a given target size T and the descent is 0.GlyphAssembly is horizontal, the width is glyph assembly stretch size for a given target size T while the ascent (respectively descent) is the maximum ascent (respectively descent) of the glyphs of id GlyphPartRecord.glyphID for all the GlyphPartRecord in GlyphAssembly.partRecords.The glyph assembly height is the sum of the glyph assembly ascent and glyph assembly descent.
Note
The horizontal (respectively vertical) metrics for a vertical (respectively horizontal) glyph assembly do not depend on the target size T.
The shaping of the glyph assembly is performed with the following algorithm:
(x, y) to (0, 0), RepetitionCounter to 0 and PartIndex to -1.RepetitionCounter is 0, then
PartIndex.PartIndex is GlyphAssembly.partCount then stop.Part to GlyphAssembly.partRecords[PartIndex]. Set RepetitionCounter to rmin if Part is an extender and to 1 otherwise.Part.glyphID so that its (left, baseline) coordinates are at position (x, y). Set x to x + Part.fullAdvance โ omaxPart.glyphID so that its (left, bottom) coordinates are at position (x, y). Set y to y โ Part.fullAdvance + omaxRepetitionCounter.The preferred inline size of a glyph stretched along the block axis is calculated using the following algorithm:
S to the glyph's advance width.MathGlyphConstruction table in the MathVariants.vertGlyphConstructionOffsets table for the given glyph:
MathGlyphVariantRecord in MathGlyphConstruction.mathGlyphVariantRecord, ensure that S is at least the advance width of the glyph of id MathGlyphVariantRecord.variantGlyph.GlyphAssembly subtable, then ensure that S is at least the glyph assembly width.S.The algorithm to shape a stretchy glyph to inline (respectively block) dimension T is the following:
MathGlyphConstruction table in the MathVariants.horizGlyphConstructionOffsets table (respectively MathVariants.vertGlyphConstructionOffsets table) for the given glyph the exit with failure.T then use normal shaping and bounding box for that glyph, the MathItalicsCorrectionInfo for that glyph as italic correction and exit with success.MathGlyphVariantRecord in MathGlyphConstruction.mathGlyphVariantRecord. If one MathGlyphVariantRecord.advanceMeasurement is at least T then use normal shaping and bounding box for MathGlyphVariantRecord.variantGlyph, the MathItalicsCorrectionInfo for that glyph as italic correction and exit with success.GlyphAssembly subtable then use the bounding box given by glyph assembly width, glyph assembly height, glyph assembly ascent, glyph assembly descent, the value GlyphAssembly.italicsCorrection as italic correction, perform shaping of the glyph assembly and exit with success.T, then choose last one that was tried and exit with success.Note
If a font does not provide tables for stretchy constructions, User Agents may use their own internal constructions as a fallback such that the one suggested in
B.4 Unicode-based Glyph Assemblies.
@namespace url(http://www.w3.org/1998/Math/MathML);
* {
font-size: math;
display: block math;
}
math {
direction: ltr;
writing-mode: horizontal-tb;
text-indent: 0;
letter-spacing: normal;
line-height: normal;
word-spacing: normal;
font-family: math;
font-size: inherit;
font-style: normal;
font-weight: normal;
display: inline math;
math-style: compact;
math-shift: normal;
math-level: 0;
}
math[display="block" i] {
display: block math;
math-style: normal;
}
math[display="inline" i] {
display: inline math;
math-style: compact;
}
semantics > :not(:first-child) {
display: none;
}
maction > :not(:first-child) {
display: none;
}
merror {
border: 1px solid red;
background-color: lightYellow;
}
mphantom {
visibility: hidden;
}
mi {
text-transform: math-auto;
}
mtable {
display: inline-table;
math-style: compact;
}
mtr {
display: table-row;
}
mtd {
display: table-cell;
text-align: center;
padding: 0.5ex 0.4em;
}
mfrac {
padding-inline-start: 1px;
padding-inline-end: 1px;
}
mfrac > * {
math-depth: auto-add;
math-style: compact;
}
mfrac > :nth-child(2) {
math-shift: compact;
}
mroot > :not(:first-child) {
math-depth: add(2);
math-style: compact;
}
mroot, msqrt {
math-shift: compact;
}
msub > :not(:first-child),
msup > :not(:first-child),
msubsup > :not(:first-child),
mmultiscripts > :not(:first-child),
munder > :not(:first-child),
mover > :not(:first-child),
munderover > :not(:first-child) {
math-depth: add(1);
math-style: compact;
}
munder[accentunder="true" i] > :nth-child(2),
mover[accent="true" i] > :nth-child(2),
munderover[accentunder="true" i] > :nth-child(2),
munderover[accent="true" i] > :nth-child(3) {
font-size: inherit;
}
msub > :nth-child(2),
msubsup > :nth-child(2),
mmultiscripts > :nth-child(even),
mmultiscripts > mprescripts ~ :nth-child(odd),
mover[accent="true" i] > :first-child,
munderover[accent="true" i] > :first-child {
math-shift: compact;
}
mmultiscripts > mprescripts ~ :nth-child(even) {
math-shift: inherit;
}The algorithm to set the properties of an operator from its category is as follows:
minsize to 1em.maxsize to โ.lspace and rspace to the value specified in the corresponding column.stretchy, symmetric, largeop, movablelimits, set that property to true if it is listed in the last column or to false otherwise.The algorithm to determine the category of an operator (Content, Form) is as folllows:
Content as an UTF-16 string does not have length or 1 or 2 then exit with category Default.Content is a single character in the range U+0320โU+03FF then exit with category Default. Otherwise, if it has two characters:
Content is the surrogate pairs corresponding to U+1EEF0 ARABIC MATHEMATICAL OPERATOR MEEM WITH HAH WITH TATWEEL or U+1EEF1 ARABIC MATHEMATICAL OPERATOR HAH WITH DAL and Form is postfix, exit with category I.Content with the first character and move to step 3.Content it is listed in Operators_2_ascii_chars then replace Content with the Unicode character "U+0320 plus the index of Content in Operators_2_ascii_chars" and move to step 3.Default.Form is infix and Content corresponds to one of U+007C VERTICAL LINE or U+223C TILDE OPERATOR then exit with category ForceDefault. If the category of (Content, Form) provided by table Figure 25 has N/A encoding in table Figure 26 (namely if it has category L or M), then exit with that category. Otherwise,
Key to Content if it is in range U+0000โU+03FF ; or to Content โ 0x1C00 if it is in range U+2000โU+2BFF. Otherwise, exit with category Default.Key according to whether Form is infix, prefix, postfix respectively.Key is at most 0x2FFF.Entry in table Figure 27 such that Entry % 0x4000 is equal to Key. If one is found then return the category corresponding to encoding Entry / 0x1000 in Figure 26. Otherwise, return category Default.Operators_2_ascii_chars 18 entries (2-characters ASCII strings): '!!', '!=', '&&', '**', '*=', '++', '+=', '--', '-=', '->', '//', '/=', ':=', '<=', '<>', '==', '>=', '||', Operators_fence 61 entries (16 Unicode ranges): [U+0028โU+0029], {U+005B}, {U+005D}, [U+007BโU+007D], {U+0331}, {U+2016}, [U+2018โU+2019], [U+201CโU+201D], [U+2308โU+230B], [U+2329โU+232A], [U+2772โU+2773], [U+27E6โU+27EF], {U+2980}, [U+2983โU+2999], [U+29D8โU+29DB], [U+29FCโU+29FD], Operators_separator 3 entries: U+002C, U+003B, U+2063, Figure 24 Special tables for the operator dictionary.[U+2190โU+2195], [U+219AโU+21AE], [U+21B0โU+21B5], {U+21B9}, [U+21BCโU+21D5], [U+21DAโU+21F0], [U+21F3โU+21FF], {U+2794}, {U+2799}, [U+279BโU+27A1], [U+27A5โU+27A6], [U+27A8โU+27AF], {U+27B1}, {U+27B3}, {U+27B5}, {U+27B8}, [U+27BAโU+27BE], [U+27F0โU+27F1], [U+27F4โU+27FF], [U+2900โU+2920], [U+2934โU+2937], [U+2942โU+2975], [U+297CโU+297F], [U+2B04โU+2B07], [U+2B0CโU+2B11], [U+2B30โU+2B3E], [U+2B40โU+2B4C], [U+2B60โU+2B65], [U+2B6AโU+2B6D], [U+2B70โU+2B73], [U+2B7AโU+2B7D], [U+2B80โU+2B87], {U+2B95}, [U+2BA0โU+2BAF], {U+2BB8}, A 109 entries (32 Unicode ranges) in infix form: {U+002B}, {U+002D}, {U+002F}, {U+00B1}, {U+00F7}, {U+0322}, {U+2044}, [U+2212โU+2216], [U+2227โU+222A], {U+2236}, {U+2238}, [U+228CโU+228E], [U+2293โU+2296], {U+2298}, [U+229DโU+229F], [U+22BBโU+22BD], [U+22CEโU+22CF], [U+22D2โU+22D3], [U+2795โU+2797], {U+29B8}, {U+29BC}, [U+29C4โU+29C5], [U+29F5โU+29FB], [U+2A1FโU+2A2E], [U+2A38โU+2A3A], {U+2A3E}, [U+2A40โU+2A4F], [U+2A51โU+2A63], {U+2ADB}, {U+2AF6}, {U+2AFB}, {U+2AFD}, B 64 entries (33 Unicode ranges) in infix form: {U+0025}, {U+002A}, {U+002E}, [U+003FโU+0040], {U+005E}, {U+00B7}, {U+00D7}, {U+0323}, {U+032E}, {U+2022}, {U+2043}, [U+2217โU+2219], {U+2240}, {U+2297}, [U+2299โU+229B], [U+22A0โU+22A1], {U+22BA}, [U+22C4โU+22C7], [U+22C9โU+22CC], [U+2305โU+2306], {U+27CB}, {U+27CD}, [U+29C6โU+29C8], [U+29D4โU+29D7], {U+29E2}, [U+2A1DโU+2A1E], [U+2A2FโU+2A37], [U+2A3BโU+2A3D], {U+2A3F}, {U+2A50}, [U+2A64โU+2A65], [U+2ADCโU+2ADD], {U+2AFE}, C 52 entries (22 Unicode ranges) in prefix form: {U+0021}, {U+002B}, {U+002D}, {U+00AC}, {U+00B1}, {U+0331}, {U+2018}, {U+201C}, [U+2200โU+2201], [U+2203โU+2204], {U+2207}, [U+2212โU+2213], [U+221FโU+2222], [U+2234โU+2235], {U+223C}, [U+22BEโU+22BF], {U+2310}, {U+2319}, [U+2795โU+2796], {U+27C0}, [U+299BโU+29AF], [U+2AECโU+2AED], D 40 entries (21 Unicode ranges) in postfix form: [U+0021โU+0022], [U+0025โU+0027], {U+0060}, {U+00A8}, {U+00B0}, [U+00B2โU+00B4], [U+00B8โU+00B9], [U+02CAโU+02CB], [U+02D8โU+02DA], {U+02DD}, {U+0311}, {U+0320}, {U+0325}, {U+0327}, {U+0331}, [U+2019โU+201B], [U+201DโU+201F], [U+2032โU+2037], {U+2057}, [U+20DBโU+20DC], {U+23CD}, E 30 entries in prefix form: U+0028, U+005B, U+007B, U+007C, U+2016, U+2308, U+230A, U+2329, U+2772, U+27E6, U+27E8, U+27EA, U+27EC, U+27EE, U+2980, U+2983, U+2985, U+2987, U+2989, U+298B, U+298D, U+298F, U+2991, U+2993, U+2995, U+2997, U+2999, U+29D8, U+29DA, U+29FC, F 30 entries in postfix form: U+0029, U+005D, U+007C, U+007D, U+2016, U+2309, U+230B, U+232A, U+2773, U+27E7, U+27E9, U+27EB, U+27ED, U+27EF, U+2980, U+2984, U+2986, U+2988, U+298A, U+298C, U+298E, U+2990, U+2992, U+2994, U+2996, U+2998, U+2999, U+29D9, U+29DB, U+29FD, G 27 entries (2 Unicode ranges) in prefix form: [U+222BโU+2233], [U+2A0BโU+2A1C], H 22 entries (13 Unicode ranges) in postfix form: [U+005EโU+005F], {U+007E}, {U+00AF}, [U+02C6โU+02C7], {U+02C9}, {U+02CD}, {U+02DC}, {U+02F7}, {U+0302}, {U+203E}, [U+2322โU+2323], [U+23B4โU+23B5], [U+23DCโU+23E1], I 22 entries (6 Unicode ranges) in prefix form: [U+220FโU+2211], [U+22C0โU+22C3], [U+2A00โU+2A0A], [U+2A1DโU+2A1E], {U+2AFC}, {U+2AFF}, J 7 entries (4 Unicode ranges) in infix form: {U+005C}, {U+005F}, [U+2061โU+2064], {U+2206}, K 6 entries (3 Unicode ranges) in prefix form: [U+2145โU+2146], {U+2202}, [U+221AโU+221C], L 3 entries in infix form: U+002C, U+003A, U+003B, M Figure 25 Mapping from operator (Content, Form) to a category.0.2777777777777778em 0.2777777777777778em N/A A infix 0x0 0.2777777777777778em 0.2777777777777778em stretchy B infix 0x4 0.2222222222222222em 0.2222222222222222em N/A C infix 0x8 0.16666666666666666em 0.16666666666666666em N/A D prefix 0x1 0 0 N/A E postfix 0x2 0 0 N/A F prefix 0x5 0 0 stretchy symmetric G postfix 0x6 0 0 stretchy symmetric H prefix 0x9 0.16666666666666666em 0.16666666666666666em symmetric largeop I postfix 0xA 0 0 stretchy J prefix 0xD 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits K infix 0xC 0 0 N/A L prefix N/A 0.16666666666666666em 0 N/A M infix N/A 0 0.16666666666666666em N/A Figure 26 Operators values for each category.{0x8025}, {0x802A}, {0x402B}, {0x402D}, {0x802E}, {0x402F}, [0x803Fโ0x8040], {0xC05C}, {0x805E}, {0xC05F}, {0x40B1}, {0x80B7}, {0x80D7}, {0x40F7}, {0x4322}, {0x8323}, {0x832E}, {0x8422}, {0x8443}, {0x4444}, [0xC461โ0xC464], [0x0590โ0x0595], [0x059Aโ0x05A9], [0x05AAโ0x05AE], [0x05B0โ0x05B5], {0x05B9}, [0x05BCโ0x05CB], [0x05CCโ0x05D5], [0x05DAโ0x05E9], [0x05EAโ0x05F0], [0x05F3โ0x05FF], {0xC606}, [0x4612โ0x4616], [0x8617โ0x8619], [0x4627โ0x462A], {0x4636}, {0x4638}, {0x8640}, [0x468Cโ0x468E], [0x4693โ0x4696], {0x8697}, {0x4698}, [0x8699โ0x869B], [0x469Dโ0x469F], [0x86A0โ0x86A1], {0x86BA}, [0x46BBโ0x46BD], [0x86C4โ0x86C7], [0x86C9โ0x86CC], [0x46CEโ0x46CF], [0x46D2โ0x46D3], [0x8705โ0x8706], {0x0B94}, [0x4B95โ0x4B97], {0x0B99}, [0x0B9Bโ0x0BA1], [0x0BA5โ0x0BA6], [0x0BA8โ0x0BAF], {0x0BB1}, {0x0BB3}, {0x0BB5}, {0x0BB8}, [0x0BBAโ0x0BBE], {0x8BCB}, {0x8BCD}, [0x0BF0โ0x0BF1], [0x0BF4โ0x0BFF], [0x0D00โ0x0D0F], [0x0D10โ0x0D1F], {0x0D20}, [0x0D34โ0x0D37], [0x0D42โ0x0D51], [0x0D52โ0x0D61], [0x0D62โ0x0D71], [0x0D72โ0x0D75], [0x0D7Cโ0x0D7F], {0x4DB8}, {0x4DBC}, [0x4DC4โ0x4DC5], [0x8DC6โ0x8DC8], [0x8DD4โ0x8DD7], {0x8DE2}, [0x4DF5โ0x4DFB], [0x8E1Dโ0x8E1E], [0x4E1Fโ0x4E2E], [0x8E2Fโ0x8E37], [0x4E38โ0x4E3A], [0x8E3Bโ0x8E3D], {0x4E3E}, {0x8E3F}, [0x4E40โ0x4E4F], {0x8E50}, [0x4E51โ0x4E60], [0x4E61โ0x4E63], [0x8E64โ0x8E65], {0x4EDB}, [0x8EDCโ0x8EDD], {0x4EF6}, {0x4EFB}, {0x4EFD}, {0x8EFE}, [0x0F04โ0x0F07], [0x0F0Cโ0x0F11], [0x0F30โ0x0F3E], [0x0F40โ0x0F4C], [0x0F60โ0x0F65], [0x0F6Aโ0x0F6D], [0x0F70โ0x0F73], [0x0F7Aโ0x0F7D], [0x0F80โ0x0F87], {0x0F95}, [0x0FA0โ0x0FAF], {0x0FB8}, {0x1021}, {0x5028}, {0x102B}, {0x102D}, {0x505B}, [0x507Bโ0x507C], {0x10AC}, {0x10B1}, {0x1331}, {0x5416}, {0x1418}, {0x141C}, [0x1600โ0x1601], [0x1603โ0x1604], {0x1607}, [0xD60Fโ0xD611], [0x1612โ0x1613], [0x161Fโ0x1622], [0x962Bโ0x9633], [0x1634โ0x1635], {0x163C}, [0x16BEโ0x16BF], [0xD6C0โ0xD6C3], {0x5708}, {0x570A}, {0x1710}, {0x1719}, {0x5729}, {0x5B72}, [0x1B95โ0x1B96], {0x1BC0}, {0x5BE6}, {0x5BE8}, {0x5BEA}, {0x5BEC}, {0x5BEE}, {0x5D80}, {0x5D83}, {0x5D85}, {0x5D87}, {0x5D89}, {0x5D8B}, {0x5D8D}, {0x5D8F}, {0x5D91}, {0x5D93}, {0x5D95}, {0x5D97}, {0x5D99}, [0x1D9Bโ0x1DAA], [0x1DABโ0x1DAF], {0x5DD8}, {0x5DDA}, {0x5DFC}, [0xDE00โ0xDE0A], [0x9E0Bโ0x9E1A], [0x9E1Bโ0x9E1C], [0xDE1Dโ0xDE1E], [0x1EECโ0x1EED], {0xDEFC}, {0xDEFF}, [0x2021โ0x2022], [0x2025โ0x2027], {0x6029}, {0x605D}, [0xA05Eโ0xA05F], {0x2060}, [0x607Cโ0x607D], {0xA07E}, {0x20A8}, {0xA0AF}, {0x20B0}, [0x20B2โ0x20B4], [0x20B8โ0x20B9], [0xA2C6โ0xA2C7], {0xA2C9}, [0x22CAโ0x22CB], {0xA2CD}, [0x22D8โ0x22DA], {0xA2DC}, {0x22DD}, {0xA2F7}, {0xA302}, {0x2311}, {0x2320}, {0x2325}, {0x2327}, {0x2331}, {0x6416}, [0x2419โ0x241B], [0x241Dโ0x241F], [0x2432โ0x2437], {0xA43E}, {0x2457}, [0x24DBโ0x24DC], {0x6709}, {0x670B}, [0xA722โ0xA723], {0x672A}, [0xA7B4โ0xA7B5], {0x27CD}, [0xA7DCโ0xA7E1], {0x6B73}, {0x6BE7}, {0x6BE9}, {0x6BEB}, {0x6BED}, {0x6BEF}, {0x6D80}, {0x6D84}, {0x6D86}, {0x6D88}, {0x6D8A}, {0x6D8C}, {0x6D8E}, {0x6D90}, {0x6D92}, {0x6D94}, {0x6D96}, [0x6D98โ0x6D99], {0x6DD9}, {0x6DDB}, {0x6DFD}, Figure 27 List of entries for the largest categories, sorted by key.Key is Entry % 0x4000, category encoding is Entry / 0x1000.Note
The intrinsic stretch axis a Unicode character c is inline if it belongs to the list below. Otherwise, the intrinsic stretch axis of c is block.
U+003D, U+005E, U+005F, U+007E, U+00AF, U+02C6, U+02C7, U+02C9, U+02CD, U+02DC, U+02F7, U+0302, U+0332, U+203E, U+20D0, U+20D1, U+20D6, U+20D7, U+20E1, U+2190, U+2192, U+2194, U+2198, U+2199, U+219A, U+219B, U+219C, U+219D, U+219E, U+21A0, U+21A2, U+21A3, U+21A4, U+21A6, U+21A9, U+21AA, U+21AB, U+21AC, U+21AD, U+21AE, U+21B4, U+21B9, U+21BC, U+21BD, U+21C0, U+21C1, U+21C4, U+21C6, U+21C7, U+21C9, U+21CB, U+21CC, U+21CD, U+21CE, U+21CF, U+21D0, U+21D2, U+21D4, U+21DA, U+21DB, U+21DC, U+21DD, U+21E0, U+21E2, U+21E4, U+21E5, U+21E6, U+21E8, U+21F0, U+21F4, U+21F6, U+21F7, U+21F8, U+21F9, U+21FA, U+21FB, U+21FC, U+21FD, U+21FE, U+21FF, U+2322, U+2323, U+23B4, U+23B5, U+23DC, U+23DD, U+23DE, U+23DF, U+23E0, U+23E1, U+2500, U+2794, U+2799, U+279B, U+279C, U+279D, U+279E, U+279F, U+27A0, U+27A1, U+27A5, U+27A6, U+27A8, U+27A9, U+27AA, U+27AB, U+27AC, U+27AD, U+27AE, U+27AF, U+27B1, U+27B3, U+27B5, U+27B8, U+27BA, U+27BB, U+27BC, U+27BD, U+27BE, U+27F4, U+27F5, U+27F6, U+27F7, U+27F8, U+27F9, U+27FA, U+27FB, U+27FC, U+27FD, U+27FE, U+27FF, U+2900, U+2901, U+2902, U+2903, U+2904, U+2905, U+2906, U+2907, U+290C, U+290D, U+290E, U+290F, U+2910, U+2911, U+2914, U+2915, U+2916, U+2917, U+2918, U+2919, U+291A, U+291B, U+291C, U+291D, U+291E, U+291F, U+2920, U+2942, U+2943, U+2944, U+2945, U+2946, U+2947, U+2948, U+294A, U+294B, U+294E, U+2950, U+2952, U+2953, U+2956, U+2957, U+295A, U+295B, U+295E, U+295F, U+2962, U+2964, U+2966, U+2967, U+2968, U+2969, U+296A, U+296B, U+296C, U+296D, U+2970, U+2971, U+2972, U+2973, U+2974, U+2975, U+297C, U+297D, U+2B04, U+2B05, U+2B0C, U+2B30, U+2B31, U+2B32, U+2B33, U+2B34, U+2B35, U+2B36, U+2B37, U+2B38, U+2B39, U+2B3A, U+2B3B, U+2B3C, U+2B3D, U+2B3E, U+2B40, U+2B41, U+2B42, U+2B43, U+2B44, U+2B45, U+2B46, U+2B47, U+2B48, U+2B49, U+2B4A, U+2B4B, U+2B4C, U+2B60, U+2B62, U+2B64, U+2B6A, U+2B6C, U+2B70, U+2B72, U+2B7A, U+2B7C, U+2B80, U+2B82, U+2B84, U+2B86, U+2B95, U+FE35, U+FE36, U+FE37, U+FE38, U+1EEF0, U+1EEF1, Figure 28 Sorted list of unicode code points corresponding to operators with inline stretch axis.Note
The intrinsic stretch axis could be included as a boolean property of the operator dictionary. But since it does not depend on the form and since very few operators can stretch along the
inline axis, it is better implemented as a separate sorted array. Each entry can be encoded with 16 bytes if U+1EEF0 ARABIC MATHEMATICAL OPERATOR MEEM WITH HAH WITH TATWEEL and U+1EEF1 ARABIC MATHEMATICAL OPERATOR HAH WITH DAL are tested separately.
This section is non-normative.
The following dictionary provides a human-readable version of B.1 Operator Dictionary. Please refer to 3.2.4.2 Dictionary-based attributes for explanation about how to use this dictionary and how to determine the values Content and Form indexing together the dictionary.
The values for rspace and lspace are indicated in the corresponding columns. The values of stretchysymmetriclargeopmovablelimitstrue if they are listed in the "properties" column.
infix 0.2777777777777778em 0.2777777777777778em N/A = U+003D inline infix 0.2777777777777778em 0.2777777777777778em N/A > U+003E block infix 0.2777777777777778em 0.2777777777777778em N/A | U+007C block infix 0.2777777777777778em 0.2777777777777778em fence โ U+2196 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2197 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2198 inline infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2199 inline infix 0.2777777777777778em 0.2777777777777778em N/A โฏ U+21AF block infix 0.2777777777777778em 0.2777777777777778em N/A โถ U+21B6 block infix 0.2777777777777778em 0.2777777777777778em N/A โท U+21B7 block infix 0.2777777777777778em 0.2777777777777778em N/A โธ U+21B8 block infix 0.2777777777777778em 0.2777777777777778em N/A โบ U+21BA block infix 0.2777777777777778em 0.2777777777777778em N/A โป U+21BB block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+21D6 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+21D7 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+21D8 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+21D9 block infix 0.2777777777777778em 0.2777777777777778em N/A โฑ U+21F1 block infix 0.2777777777777778em 0.2777777777777778em N/A โฒ U+21F2 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2208 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2209 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+220A block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+220B block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+220C block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+220D block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+221D block infix 0.2777777777777778em 0.2777777777777778em N/A โฃ U+2223 block infix 0.2777777777777778em 0.2777777777777778em N/A โค U+2224 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅ U+2225 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆ U+2226 block infix 0.2777777777777778em 0.2777777777777778em N/A โท U+2237 block infix 0.2777777777777778em 0.2777777777777778em N/A โน U+2239 block infix 0.2777777777777778em 0.2777777777777778em N/A โบ U+223A block infix 0.2777777777777778em 0.2777777777777778em N/A โป U+223B block infix 0.2777777777777778em 0.2777777777777778em N/A โผ U+223C block infix 0.2777777777777778em 0.2777777777777778em N/A โฝ U+223D block infix 0.2777777777777778em 0.2777777777777778em N/A โพ U+223E block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2241 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2242 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2243 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2244 block infix 0.2777777777777778em 0.2777777777777778em N/A โ
U+2245 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2246 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2247 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2248 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2249 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+224A block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+224B block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+224C block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+224D block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+224E block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+224F block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2250 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2251 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2252 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2253 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2254 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2255 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2256 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2257 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2258 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2259 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+225A block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+225B block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+225C block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+225D block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+225E block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+225F block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2260 block infix 0.2777777777777778em 0.2777777777777778em N/A โก U+2261 block infix 0.2777777777777778em 0.2777777777777778em N/A โข U+2262 block infix 0.2777777777777778em 0.2777777777777778em N/A โฃ U+2263 block infix 0.2777777777777778em 0.2777777777777778em N/A โค U+2264 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅ U+2265 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆ U+2266 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+2267 block infix 0.2777777777777778em 0.2777777777777778em N/A โจ U+2268 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉ U+2269 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+226A block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+226B block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+226C block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+226D block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+226E block infix 0.2777777777777778em 0.2777777777777778em N/A โฏ U+226F block infix 0.2777777777777778em 0.2777777777777778em N/A โฐ U+2270 block infix 0.2777777777777778em 0.2777777777777778em N/A โฑ U+2271 block infix 0.2777777777777778em 0.2777777777777778em N/A โฒ U+2272 block infix 0.2777777777777778em 0.2777777777777778em N/A โณ U+2273 block infix 0.2777777777777778em 0.2777777777777778em N/A โด U+2274 block infix 0.2777777777777778em 0.2777777777777778em N/A โต U+2275 block infix 0.2777777777777778em 0.2777777777777778em N/A โถ U+2276 block infix 0.2777777777777778em 0.2777777777777778em N/A โท U+2277 block infix 0.2777777777777778em 0.2777777777777778em N/A โธ U+2278 block infix 0.2777777777777778em 0.2777777777777778em N/A โน U+2279 block infix 0.2777777777777778em 0.2777777777777778em N/A โบ U+227A block infix 0.2777777777777778em 0.2777777777777778em N/A โป U+227B block infix 0.2777777777777778em 0.2777777777777778em N/A โผ U+227C block infix 0.2777777777777778em 0.2777777777777778em N/A โฝ U+227D block infix 0.2777777777777778em 0.2777777777777778em N/A โพ U+227E block infix 0.2777777777777778em 0.2777777777777778em N/A โฟ U+227F block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2280 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2281 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2282 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2283 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2284 block infix 0.2777777777777778em 0.2777777777777778em N/A โ
U+2285 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2286 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2287 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2288 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2289 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+228A block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+228B block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+228F block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2290 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2291 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2292 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+229C block infix 0.2777777777777778em 0.2777777777777778em N/A โข U+22A2 block infix 0.2777777777777778em 0.2777777777777778em N/A โฃ U+22A3 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆ U+22A6 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+22A7 block infix 0.2777777777777778em 0.2777777777777778em N/A โจ U+22A8 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉ U+22A9 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+22AA block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+22AB block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+22AC block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+22AD block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+22AE block infix 0.2777777777777778em 0.2777777777777778em N/A โฏ U+22AF block infix 0.2777777777777778em 0.2777777777777778em N/A โฐ U+22B0 block infix 0.2777777777777778em 0.2777777777777778em N/A โฑ U+22B1 block infix 0.2777777777777778em 0.2777777777777778em N/A โฒ U+22B2 block infix 0.2777777777777778em 0.2777777777777778em N/A โณ U+22B3 block infix 0.2777777777777778em 0.2777777777777778em N/A โด U+22B4 block infix 0.2777777777777778em 0.2777777777777778em N/A โต U+22B5 block infix 0.2777777777777778em 0.2777777777777778em N/A โถ U+22B6 block infix 0.2777777777777778em 0.2777777777777778em N/A โท U+22B7 block infix 0.2777777777777778em 0.2777777777777778em N/A โธ U+22B8 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22C8 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22CD block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D0 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D1 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D4 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D5 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D6 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D7 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D8 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22D9 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22DA block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22DB block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22DC block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22DD block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22DE block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22DF block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+22E0 block infix 0.2777777777777778em 0.2777777777777778em N/A โก U+22E1 block infix 0.2777777777777778em 0.2777777777777778em N/A โข U+22E2 block infix 0.2777777777777778em 0.2777777777777778em N/A โฃ U+22E3 block infix 0.2777777777777778em 0.2777777777777778em N/A โค U+22E4 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅ U+22E5 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆ U+22E6 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+22E7 block infix 0.2777777777777778em 0.2777777777777778em N/A โจ U+22E8 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉ U+22E9 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+22EA block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+22EB block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+22EC block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+22ED block infix 0.2777777777777778em 0.2777777777777778em N/A โฒ U+22F2 block infix 0.2777777777777778em 0.2777777777777778em N/A โณ U+22F3 block infix 0.2777777777777778em 0.2777777777777778em N/A โด U+22F4 block infix 0.2777777777777778em 0.2777777777777778em N/A โต U+22F5 block infix 0.2777777777777778em 0.2777777777777778em N/A โถ U+22F6 block infix 0.2777777777777778em 0.2777777777777778em N/A โท U+22F7 block infix 0.2777777777777778em 0.2777777777777778em N/A โธ U+22F8 block infix 0.2777777777777778em 0.2777777777777778em N/A โน U+22F9 block infix 0.2777777777777778em 0.2777777777777778em N/A โบ U+22FA block infix 0.2777777777777778em 0.2777777777777778em N/A โป U+22FB block infix 0.2777777777777778em 0.2777777777777778em N/A โผ U+22FC block infix 0.2777777777777778em 0.2777777777777778em N/A โฝ U+22FD block infix 0.2777777777777778em 0.2777777777777778em N/A โพ U+22FE block infix 0.2777777777777778em 0.2777777777777778em N/A โฟ U+22FF block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2301 block infix 0.2777777777777778em 0.2777777777777778em N/A โผ U+237C block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+238B block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+2798 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+279A block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+27A7 block infix 0.2777777777777778em 0.2777777777777778em N/A โฒ U+27B2 block infix 0.2777777777777778em 0.2777777777777778em N/A โด U+27B4 block infix 0.2777777777777778em 0.2777777777777778em N/A โถ U+27B6 block infix 0.2777777777777778em 0.2777777777777778em N/A โท U+27B7 block infix 0.2777777777777778em 0.2777777777777778em N/A โน U+27B9 block infix 0.2777777777777778em 0.2777777777777778em N/A โ U+27C2 block infix 0.2777777777777778em 0.2777777777777778em N/A โฒ U+27F2 block infix 0.2777777777777778em 0.2777777777777778em N/A โณ U+27F3 block infix 0.2777777777777778em 0.2777777777777778em N/A โคก U+2921 block infix 0.2777777777777778em 0.2777777777777778em N/A โคข U+2922 block infix 0.2777777777777778em 0.2777777777777778em N/A โคฃ U+2923 block infix 0.2777777777777778em 0.2777777777777778em N/A โคค U+2924 block infix 0.2777777777777778em 0.2777777777777778em N/A โคฅ U+2925 block infix 0.2777777777777778em 0.2777777777777778em N/A โคฆ U+2926 block infix 0.2777777777777778em 0.2777777777777778em N/A โคง U+2927 block infix 0.2777777777777778em 0.2777777777777778em N/A โคจ U+2928 block infix 0.2777777777777778em 0.2777777777777778em N/A โคฉ U+2929 block infix 0.2777777777777778em 0.2777777777777778em N/A โคช U+292A block infix 0.2777777777777778em 0.2777777777777778em N/A โคซ U+292B block infix 0.2777777777777778em 0.2777777777777778em N/A โคฌ U+292C block infix 0.2777777777777778em 0.2777777777777778em N/A โคญ U+292D block infix 0.2777777777777778em 0.2777777777777778em N/A โคฎ U+292E block infix 0.2777777777777778em 0.2777777777777778em N/A โคฏ U+292F block infix 0.2777777777777778em 0.2777777777777778em N/A โคฐ U+2930 block infix 0.2777777777777778em 0.2777777777777778em N/A โคฑ U+2931 block infix 0.2777777777777778em 0.2777777777777778em N/A โคฒ U+2932 block infix 0.2777777777777778em 0.2777777777777778em N/A โคณ U+2933 block infix 0.2777777777777778em 0.2777777777777778em N/A โคธ U+2938 block infix 0.2777777777777778em 0.2777777777777778em N/A โคน U+2939 block infix 0.2777777777777778em 0.2777777777777778em N/A โคบ U+293A block infix 0.2777777777777778em 0.2777777777777778em N/A โคป U+293B block infix 0.2777777777777778em 0.2777777777777778em N/A โคผ U+293C block infix 0.2777777777777778em 0.2777777777777778em N/A โคฝ U+293D block infix 0.2777777777777778em 0.2777777777777778em N/A โคพ U+293E block infix 0.2777777777777778em 0.2777777777777778em N/A โคฟ U+293F block infix 0.2777777777777778em 0.2777777777777778em N/A โฅ U+2940 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅ U+2941 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅถ U+2976 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅท U+2977 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅธ U+2978 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅน U+2979 block infix 0.2777777777777778em 0.2777777777777778em N/A โฅบ U+297A block infix 0.2777777777777778em 0.2777777777777778em N/A โฅป U+297B block infix 0.2777777777777778em 0.2777777777777778em N/A โฆ U+2981 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆ U+2982 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆถ U+29B6 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆท U+29B7 block infix 0.2777777777777778em 0.2777777777777778em N/A โฆน U+29B9 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29C0 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29C1 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29CE block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29CF block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29D0 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29D1 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29D2 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29D3 block infix 0.2777777777777778em 0.2777777777777778em N/A โง U+29DF block infix 0.2777777777777778em 0.2777777777777778em N/A โงก U+29E1 block infix 0.2777777777777778em 0.2777777777777778em N/A โงฃ U+29E3 block infix 0.2777777777777778em 0.2777777777777778em N/A โงค U+29E4 block infix 0.2777777777777778em 0.2777777777777778em N/A โงฅ U+29E5 block infix 0.2777777777777778em 0.2777777777777778em N/A โงฆ U+29E6 block infix 0.2777777777777778em 0.2777777777777778em N/A โงด U+29F4 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฆ U+2A66 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉง U+2A67 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉจ U+2A68 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฉ U+2A69 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉช U+2A6A block infix 0.2777777777777778em 0.2777777777777778em N/A โฉซ U+2A6B block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฌ U+2A6C block infix 0.2777777777777778em 0.2777777777777778em N/A โฉญ U+2A6D block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฎ U+2A6E block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฏ U+2A6F block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฐ U+2A70 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฑ U+2A71 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฒ U+2A72 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉณ U+2A73 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉด U+2A74 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉต U+2A75 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉถ U+2A76 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉท U+2A77 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉธ U+2A78 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉน U+2A79 block infix 0.2777777777777778em 0.2777777777777778em N/A โฉบ U+2A7A block infix 0.2777777777777778em 0.2777777777777778em N/A โฉป U+2A7B block infix 0.2777777777777778em 0.2777777777777778em N/A โฉผ U+2A7C block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฝ U+2A7D block infix 0.2777777777777778em 0.2777777777777778em N/A โฉพ U+2A7E block infix 0.2777777777777778em 0.2777777777777778em N/A โฉฟ U+2A7F block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A80 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A81 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A82 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A83 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A84 block infix 0.2777777777777778em 0.2777777777777778em N/A โช
U+2A85 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A86 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A87 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A88 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A89 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A8A block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A8B block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A8C block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A8D block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A8E block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A8F block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A90 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A91 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A92 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A93 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A94 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A95 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A96 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A97 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A98 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A99 block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A9A block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A9B block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A9C block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A9D block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A9E block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2A9F block infix 0.2777777777777778em 0.2777777777777778em N/A โช U+2AA0 block infix 0.2777777777777778em 0.2777777777777778em N/A โชก U+2AA1 block infix 0.2777777777777778em 0.2777777777777778em N/A โชข U+2AA2 block infix 0.2777777777777778em 0.2777777777777778em N/A โชฃ U+2AA3 block infix 0.2777777777777778em 0.2777777777777778em N/A โชค U+2AA4 block infix 0.2777777777777778em 0.2777777777777778em N/A โชฅ U+2AA5 block infix 0.2777777777777778em 0.2777777777777778em N/A โชฆ U+2AA6 block infix 0.2777777777777778em 0.2777777777777778em N/A โชง U+2AA7 block infix 0.2777777777777778em 0.2777777777777778em N/A โชจ U+2AA8 block infix 0.2777777777777778em 0.2777777777777778em N/A โชฉ U+2AA9 block infix 0.2777777777777778em 0.2777777777777778em N/A โชช U+2AAA block infix 0.2777777777777778em 0.2777777777777778em N/A โชซ U+2AAB block infix 0.2777777777777778em 0.2777777777777778em N/A โชฌ U+2AAC block infix 0.2777777777777778em 0.2777777777777778em N/A โชญ U+2AAD block infix 0.2777777777777778em 0.2777777777777778em N/A โชฎ U+2AAE block infix 0.2777777777777778em 0.2777777777777778em N/A โชฏ U+2AAF block infix 0.2777777777777778em 0.2777777777777778em N/A โชฐ U+2AB0 block infix 0.2777777777777778em 0.2777777777777778em N/A โชฑ U+2AB1 block infix 0.2777777777777778em 0.2777777777777778em N/A โชฒ U+2AB2 block infix 0.2777777777777778em 0.2777777777777778em N/A โชณ U+2AB3 block infix 0.2777777777777778em 0.2777777777777778em N/A โชด U+2AB4 block infix 0.2777777777777778em 0.2777777777777778em N/A โชต U+2AB5 block infix 0.2777777777777778em 0.2777777777777778em N/A โชถ U+2AB6 block infix 0.2777777777777778em 0.2777777777777778em N/A โชท U+2AB7 block infix 0.2777777777777778em 0.2777777777777778em N/A โชธ U+2AB8 block infix 0.2777777777777778em 0.2777777777777778em N/A โชน U+2AB9 block infix 0.2777777777777778em 0.2777777777777778em N/A โชบ U+2ABA block infix 0.2777777777777778em 0.2777777777777778em N/A โชป U+2ABB block infix 0.2777777777777778em 0.2777777777777778em N/A โชผ U+2ABC block infix 0.2777777777777778em 0.2777777777777778em N/A โชฝ U+2ABD block infix 0.2777777777777778em 0.2777777777777778em N/A โชพ U+2ABE block infix 0.2777777777777778em 0.2777777777777778em N/A โชฟ U+2ABF block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC0 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC1 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC2 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC3 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC4 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ
U+2AC5 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC6 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC7 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC8 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AC9 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ACA block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ACB block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ACC block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ACD block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ACE block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ACF block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD0 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD1 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD2 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD3 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD4 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD5 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD6 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD7 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD8 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AD9 block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ADA block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ADE block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2ADF block infix 0.2777777777777778em 0.2777777777777778em N/A โซ U+2AE0 block infix 0.2777777777777778em 0.2777777777777778em N/A โซก U+2AE1 block infix 0.2777777777777778em 0.2777777777777778em N/A โซข U+2AE2 block infix 0.2777777777777778em 0.2777777777777778em N/A โซฃ U+2AE3 block infix 0.2777777777777778em 0.2777777777777778em N/A โซค U+2AE4 block infix 0.2777777777777778em 0.2777777777777778em N/A โซฅ U+2AE5 block infix 0.2777777777777778em 0.2777777777777778em N/A โซฆ U+2AE6 block infix 0.2777777777777778em 0.2777777777777778em N/A โซง U+2AE7 block infix 0.2777777777777778em 0.2777777777777778em N/A โซจ U+2AE8 block infix 0.2777777777777778em 0.2777777777777778em N/A โซฉ U+2AE9 block infix 0.2777777777777778em 0.2777777777777778em N/A โซช U+2AEA block infix 0.2777777777777778em 0.2777777777777778em N/A โซซ U+2AEB block infix 0.2777777777777778em 0.2777777777777778em N/A โซฎ U+2AEE block infix 0.2777777777777778em 0.2777777777777778em N/A โซฒ U+2AF2 block infix 0.2777777777777778em 0.2777777777777778em N/A โซณ U+2AF3 block infix 0.2777777777777778em 0.2777777777777778em N/A โซด U+2AF4 block infix 0.2777777777777778em 0.2777777777777778em N/A โซต U+2AF5 block infix 0.2777777777777778em 0.2777777777777778em N/A โซท U+2AF7 block infix 0.2777777777777778em 0.2777777777777778em N/A โซธ U+2AF8 block infix 0.2777777777777778em 0.2777777777777778em N/A โซน U+2AF9 block infix 0.2777777777777778em 0.2777777777777778em N/A โซบ U+2AFA block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B00 block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B01 block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B02 block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B03 block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B08 block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B09 block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B0A block infix 0.2777777777777778em 0.2777777777777778em N/A โฌ U+2B0B block infix 0.2777777777777778em 0.2777777777777778em N/A โฌฟ U+2B3F block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B4D block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B4E block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B4F block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B5A block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B5B block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B5C block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B5D block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B5E block infix 0.2777777777777778em 0.2777777777777778em N/A โญ U+2B5F block infix 0.2777777777777778em 0.2777777777777778em N/A โญฆ U+2B66 block infix 0.2777777777777778em 0.2777777777777778em N/A โญง U+2B67 block infix 0.2777777777777778em 0.2777777777777778em N/A โญจ U+2B68 block infix 0.2777777777777778em 0.2777777777777778em N/A โญฉ U+2B69 block infix 0.2777777777777778em 0.2777777777777778em N/A โญฎ U+2B6E block infix 0.2777777777777778em 0.2777777777777778em N/A โญฏ U+2B6F block infix 0.2777777777777778em 0.2777777777777778em N/A โญถ U+2B76 block infix 0.2777777777777778em 0.2777777777777778em N/A โญท U+2B77 block infix 0.2777777777777778em 0.2777777777777778em N/A โญธ U+2B78 block infix 0.2777777777777778em 0.2777777777777778em N/A โญน U+2B79 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B88 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B89 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B8A block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B8B block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B8C block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B8D block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B8E block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B8F block infix 0.2777777777777778em 0.2777777777777778em N/A โฎ U+2B94 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎฐ U+2BB0 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎฑ U+2BB1 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎฒ U+2BB2 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎณ U+2BB3 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎด U+2BB4 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎต U+2BB5 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎถ U+2BB6 block infix 0.2777777777777778em 0.2777777777777778em N/A โฎท U+2BB7 block infix 0.2777777777777778em 0.2777777777777778em N/A โฏ U+2BD1 block infix 0.2777777777777778em 0.2777777777777778em N/A String != U+0021 U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String *= U+002A U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String += U+002B U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String -= U+002D U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String -> U+002D U+003E block infix 0.2777777777777778em 0.2777777777777778em N/A String // U+002F U+002F block infix 0.2777777777777778em 0.2777777777777778em N/A String /= U+002F U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String := U+003A U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String <= U+003C U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String == U+003D U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String >= U+003E U+003D block infix 0.2777777777777778em 0.2777777777777778em N/A String || U+007C U+007C block infix 0.2777777777777778em 0.2777777777777778em fence โ U+2190 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2191 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2192 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2193 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2194 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2195 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+219A inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+219B inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+219C inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+219D inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+219E inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+219F block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21A0 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โก U+21A1 block infix 0.2777777777777778em 0.2777777777777778em stretchy โข U+21A2 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฃ U+21A3 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โค U+21A4 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฅ U+21A5 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฆ U+21A6 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โง U+21A7 block infix 0.2777777777777778em 0.2777777777777778em stretchy โจ U+21A8 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฉ U+21A9 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โช U+21AA inline infix 0.2777777777777778em 0.2777777777777778em stretchy โซ U+21AB inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฌ U+21AC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+21AD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+21AE inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฐ U+21B0 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฑ U+21B1 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฒ U+21B2 block infix 0.2777777777777778em 0.2777777777777778em stretchy โณ U+21B3 block infix 0.2777777777777778em 0.2777777777777778em stretchy โด U+21B4 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โต U+21B5 block infix 0.2777777777777778em 0.2777777777777778em stretchy โน U+21B9 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โผ U+21BC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฝ U+21BD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โพ U+21BE block infix 0.2777777777777778em 0.2777777777777778em stretchy โฟ U+21BF block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C0 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C1 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C2 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C3 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C4 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ
U+21C5 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C6 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C7 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C8 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21C9 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21CA block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21CB inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21CC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21CD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21CE inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21CF inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21D0 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21D1 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21D2 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21D3 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21D4 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21D5 block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21DA inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21DB inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21DC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21DD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21DE block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21DF block infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+21E0 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โก U+21E1 block infix 0.2777777777777778em 0.2777777777777778em stretchy โข U+21E2 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฃ U+21E3 block infix 0.2777777777777778em 0.2777777777777778em stretchy โค U+21E4 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฅ U+21E5 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฆ U+21E6 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โง U+21E7 block infix 0.2777777777777778em 0.2777777777777778em stretchy โจ U+21E8 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฉ U+21E9 block infix 0.2777777777777778em 0.2777777777777778em stretchy โช U+21EA block infix 0.2777777777777778em 0.2777777777777778em stretchy โซ U+21EB block infix 0.2777777777777778em 0.2777777777777778em stretchy โฌ U+21EC block infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+21ED block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+21EE block infix 0.2777777777777778em 0.2777777777777778em stretchy โฏ U+21EF block infix 0.2777777777777778em 0.2777777777777778em stretchy โฐ U+21F0 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โณ U+21F3 block infix 0.2777777777777778em 0.2777777777777778em stretchy โด U+21F4 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โต U+21F5 block infix 0.2777777777777778em 0.2777777777777778em stretchy โถ U+21F6 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โท U+21F7 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โธ U+21F8 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โน U+21F9 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โบ U+21FA inline infix 0.2777777777777778em 0.2777777777777778em stretchy โป U+21FB inline infix 0.2777777777777778em 0.2777777777777778em stretchy โผ U+21FC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฝ U+21FD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โพ U+21FE inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฟ U+21FF inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2794 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+2799 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+279B inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+279C inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+279D inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+279E inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+279F inline infix 0.2777777777777778em 0.2777777777777778em stretchy โ U+27A0 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โก U+27A1 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฅ U+27A5 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฆ U+27A6 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โจ U+27A8 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฉ U+27A9 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โช U+27AA inline infix 0.2777777777777778em 0.2777777777777778em stretchy โซ U+27AB inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฌ U+27AC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+27AD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+27AE inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฏ U+27AF inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฑ U+27B1 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โณ U+27B3 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โต U+27B5 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โธ U+27B8 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โบ U+27BA inline infix 0.2777777777777778em 0.2777777777777778em stretchy โป U+27BB inline infix 0.2777777777777778em 0.2777777777777778em stretchy โผ U+27BC inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฝ U+27BD inline infix 0.2777777777777778em 0.2777777777777778em stretchy โพ U+27BE inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฐ U+27F0 block infix 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U+2B45 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B46 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B47 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B48 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B49 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B4A inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B4B inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B4C inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญ U+2B60 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญก U+2B61 block infix 0.2777777777777778em 0.2777777777777778em stretchy โญข U+2B62 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญฃ U+2B63 block infix 0.2777777777777778em 0.2777777777777778em stretchy โญค U+2B64 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญฅ U+2B65 block infix 0.2777777777777778em 0.2777777777777778em stretchy โญช U+2B6A inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญซ U+2B6B block infix 0.2777777777777778em 0.2777777777777778em stretchy โญฌ U+2B6C inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญญ U+2B6D block infix 0.2777777777777778em 0.2777777777777778em stretchy โญฐ U+2B70 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญฑ U+2B71 block infix 0.2777777777777778em 0.2777777777777778em stretchy โญฒ U+2B72 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญณ U+2B73 block infix 0.2777777777777778em 0.2777777777777778em stretchy โญบ U+2B7A inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญป U+2B7B block infix 0.2777777777777778em 0.2777777777777778em stretchy โญผ U+2B7C inline infix 0.2777777777777778em 0.2777777777777778em stretchy โญฝ U+2B7D block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B80 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B81 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B82 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B83 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B84 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ
U+2B85 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B86 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B87 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2B95 inline infix 0.2777777777777778em 0.2777777777777778em stretchy โฎ U+2BA0 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎก U+2BA1 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎข U+2BA2 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฃ U+2BA3 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎค U+2BA4 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฅ U+2BA5 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฆ U+2BA6 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎง U+2BA7 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎจ U+2BA8 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฉ U+2BA9 block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎช U+2BAA block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎซ U+2BAB block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฌ U+2BAC block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎญ U+2BAD block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฎ U+2BAE block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎฏ U+2BAF block infix 0.2777777777777778em 0.2777777777777778em stretchy โฎธ U+2BB8 block infix 0.2777777777777778em 0.2777777777777778em stretchy + U+002B block infix 0.2222222222222222em 0.2222222222222222em N/A - U+002D block infix 0.2222222222222222em 0.2222222222222222em N/A / U+002F block infix 0.2222222222222222em 0.2222222222222222em N/A ยฑ U+00B1 block infix 0.2222222222222222em 0.2222222222222222em N/A รท U+00F7 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2044 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2212 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2213 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2214 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2215 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2216 block infix 0.2222222222222222em 0.2222222222222222em N/A โง U+2227 block infix 0.2222222222222222em 0.2222222222222222em N/A โจ U+2228 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2229 block infix 0.2222222222222222em 0.2222222222222222em N/A โช U+222A block infix 0.2222222222222222em 0.2222222222222222em N/A โถ U+2236 block infix 0.2222222222222222em 0.2222222222222222em N/A โธ U+2238 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+228C block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+228D block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+228E block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2293 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2294 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2295 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2296 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2298 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+229D block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+229E block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+229F block infix 0.2222222222222222em 0.2222222222222222em N/A โป U+22BB block infix 0.2222222222222222em 0.2222222222222222em N/A โผ U+22BC block infix 0.2222222222222222em 0.2222222222222222em N/A โฝ U+22BD block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+22CE block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+22CF block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+22D2 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+22D3 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2795 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2796 block infix 0.2222222222222222em 0.2222222222222222em N/A โ U+2797 block infix 0.2222222222222222em 0.2222222222222222em N/A โฆธ U+29B8 block infix 0.2222222222222222em 0.2222222222222222em N/A โฆผ U+29BC block infix 0.2222222222222222em 0.2222222222222222em N/A โง U+29C4 block infix 0.2222222222222222em 0.2222222222222222em N/A โง
U+29C5 block infix 0.2222222222222222em 0.2222222222222222em N/A โงต U+29F5 block infix 0.2222222222222222em 0.2222222222222222em N/A โงถ U+29F6 block infix 0.2222222222222222em 0.2222222222222222em N/A โงท U+29F7 block infix 0.2222222222222222em 0.2222222222222222em N/A โงธ U+29F8 block infix 0.2222222222222222em 0.2222222222222222em N/A โงน U+29F9 block infix 0.2222222222222222em 0.2222222222222222em N/A โงบ U+29FA block infix 0.2222222222222222em 0.2222222222222222em N/A โงป U+29FB block infix 0.2222222222222222em 0.2222222222222222em N/A โจ U+2A1F block infix 0.2222222222222222em 0.2222222222222222em N/A โจ U+2A20 block infix 0.2222222222222222em 0.2222222222222222em N/A โจก U+2A21 block infix 0.2222222222222222em 0.2222222222222222em N/A โจข U+2A22 block infix 0.2222222222222222em 0.2222222222222222em N/A โจฃ U+2A23 block infix 0.2222222222222222em 0.2222222222222222em N/A โจค U+2A24 block infix 0.2222222222222222em 0.2222222222222222em N/A โจฅ U+2A25 block infix 0.2222222222222222em 0.2222222222222222em N/A โจฆ U+2A26 block infix 0.2222222222222222em 0.2222222222222222em N/A โจง U+2A27 block infix 0.2222222222222222em 0.2222222222222222em N/A โจจ U+2A28 block infix 0.2222222222222222em 0.2222222222222222em N/A โจฉ U+2A29 block infix 0.2222222222222222em 0.2222222222222222em N/A โจช U+2A2A block infix 0.2222222222222222em 0.2222222222222222em N/A โจซ U+2A2B block infix 0.2222222222222222em 0.2222222222222222em N/A โจฌ U+2A2C block infix 0.2222222222222222em 0.2222222222222222em N/A โจญ U+2A2D block infix 0.2222222222222222em 0.2222222222222222em N/A โจฎ U+2A2E block infix 0.2222222222222222em 0.2222222222222222em N/A โจธ U+2A38 block infix 0.2222222222222222em 0.2222222222222222em N/A โจน U+2A39 block infix 0.2222222222222222em 0.2222222222222222em N/A โจบ U+2A3A block infix 0.2222222222222222em 0.2222222222222222em N/A โจพ U+2A3E block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A40 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A41 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A42 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A43 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A44 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ
U+2A45 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A46 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A47 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A48 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A49 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A4A block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A4B block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A4C block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A4D block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A4E block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A4F block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A51 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A52 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A53 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A54 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A55 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A56 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A57 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A58 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A59 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A5A block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A5B block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A5C block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A5D block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A5E block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A5F block infix 0.2222222222222222em 0.2222222222222222em N/A โฉ U+2A60 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉก U+2A61 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉข U+2A62 block infix 0.2222222222222222em 0.2222222222222222em N/A โฉฃ U+2A63 block infix 0.2222222222222222em 0.2222222222222222em N/A โซ U+2ADB block infix 0.2222222222222222em 0.2222222222222222em N/A โซถ U+2AF6 block infix 0.2222222222222222em 0.2222222222222222em N/A โซป U+2AFB block infix 0.2222222222222222em 0.2222222222222222em N/A โซฝ U+2AFD block infix 0.2222222222222222em 0.2222222222222222em N/A String && U+0026 U+0026 block infix 0.2222222222222222em 0.2222222222222222em N/A % U+0025 block infix 0.16666666666666666em 0.16666666666666666em N/A * U+002A block infix 0.16666666666666666em 0.16666666666666666em N/A . U+002E block infix 0.16666666666666666em 0.16666666666666666em N/A ? U+003F block infix 0.16666666666666666em 0.16666666666666666em N/A @ U+0040 block infix 0.16666666666666666em 0.16666666666666666em N/A ^ U+005E inline infix 0.16666666666666666em 0.16666666666666666em N/A ยท U+00B7 block infix 0.16666666666666666em 0.16666666666666666em N/A ร U+00D7 block infix 0.16666666666666666em 0.16666666666666666em N/A โข U+2022 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2043 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2217 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2218 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2219 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2240 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2297 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2299 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+229A block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+229B block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22A0 block infix 0.16666666666666666em 0.16666666666666666em N/A โก U+22A1 block infix 0.16666666666666666em 0.16666666666666666em N/A โบ U+22BA block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22C4 block infix 0.16666666666666666em 0.16666666666666666em N/A โ
U+22C5 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22C6 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22C7 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22C9 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22CA block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22CB block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+22CC block infix 0.16666666666666666em 0.16666666666666666em N/A โ
U+2305 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+2306 block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+27CB block infix 0.16666666666666666em 0.16666666666666666em N/A โ U+27CD block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29C6 block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29C7 block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29C8 block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29D4 block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29D5 block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29D6 block infix 0.16666666666666666em 0.16666666666666666em N/A โง U+29D7 block infix 0.16666666666666666em 0.16666666666666666em N/A โงข U+29E2 block infix 0.16666666666666666em 0.16666666666666666em N/A โจ U+2A1D block infix 0.16666666666666666em 0.16666666666666666em N/A โจ U+2A1E block infix 0.16666666666666666em 0.16666666666666666em N/A โจฏ U+2A2F block infix 0.16666666666666666em 0.16666666666666666em N/A โจฐ U+2A30 block infix 0.16666666666666666em 0.16666666666666666em N/A โจฑ U+2A31 block infix 0.16666666666666666em 0.16666666666666666em N/A โจฒ U+2A32 block infix 0.16666666666666666em 0.16666666666666666em N/A โจณ U+2A33 block infix 0.16666666666666666em 0.16666666666666666em N/A โจด U+2A34 block infix 0.16666666666666666em 0.16666666666666666em N/A โจต U+2A35 block infix 0.16666666666666666em 0.16666666666666666em N/A โจถ U+2A36 block infix 0.16666666666666666em 0.16666666666666666em N/A โจท U+2A37 block infix 0.16666666666666666em 0.16666666666666666em N/A โจป U+2A3B block infix 0.16666666666666666em 0.16666666666666666em N/A โจผ U+2A3C block infix 0.16666666666666666em 0.16666666666666666em N/A โจฝ U+2A3D block infix 0.16666666666666666em 0.16666666666666666em N/A โจฟ U+2A3F block infix 0.16666666666666666em 0.16666666666666666em N/A โฉ U+2A50 block infix 0.16666666666666666em 0.16666666666666666em N/A โฉค U+2A64 block infix 0.16666666666666666em 0.16666666666666666em N/A โฉฅ U+2A65 block infix 0.16666666666666666em 0.16666666666666666em N/A โซ U+2ADC block infix 0.16666666666666666em 0.16666666666666666em N/A โซ U+2ADD block infix 0.16666666666666666em 0.16666666666666666em N/A โซพ U+2AFE block infix 0.16666666666666666em 0.16666666666666666em N/A String ** U+002A U+002A block infix 0.16666666666666666em 0.16666666666666666em N/A String <> U+003C U+003E block infix 0.16666666666666666em 0.16666666666666666em N/A ! U+0021 block prefix 0 0 N/A + U+002B block prefix 0 0 N/A - U+002D block prefix 0 0 N/A ยฌ U+00AC block prefix 0 0 N/A ยฑ U+00B1 block prefix 0 0 N/A โ U+2018 block prefix 0 0 fence โ U+201C block prefix 0 0 fence โ U+2200 block prefix 0 0 N/A โ U+2201 block prefix 0 0 N/A โ U+2203 block prefix 0 0 N/A โ U+2204 block prefix 0 0 N/A โ U+2207 block prefix 0 0 N/A โ U+2212 block prefix 0 0 N/A โ U+2213 block prefix 0 0 N/A โ U+221F block prefix 0 0 N/A โ U+2220 block prefix 0 0 N/A โก U+2221 block prefix 0 0 N/A โข U+2222 block prefix 0 0 N/A โด U+2234 block prefix 0 0 N/A โต U+2235 block prefix 0 0 N/A โผ U+223C block prefix 0 0 N/A โพ U+22BE block prefix 0 0 N/A โฟ U+22BF block prefix 0 0 N/A โ U+2310 block prefix 0 0 N/A โ U+2319 block prefix 0 0 N/A โ U+2795 block prefix 0 0 N/A โ U+2796 block prefix 0 0 N/A โ U+27C0 block prefix 0 0 N/A โฆ U+299B block prefix 0 0 N/A โฆ U+299C block prefix 0 0 N/A โฆ U+299D block prefix 0 0 N/A โฆ U+299E block prefix 0 0 N/A โฆ U+299F block prefix 0 0 N/A โฆ U+29A0 block prefix 0 0 N/A โฆก U+29A1 block prefix 0 0 N/A โฆข U+29A2 block prefix 0 0 N/A โฆฃ U+29A3 block prefix 0 0 N/A โฆค U+29A4 block prefix 0 0 N/A โฆฅ U+29A5 block prefix 0 0 N/A โฆฆ U+29A6 block prefix 0 0 N/A โฆง U+29A7 block prefix 0 0 N/A โฆจ U+29A8 block prefix 0 0 N/A โฆฉ U+29A9 block prefix 0 0 N/A โฆช U+29AA block prefix 0 0 N/A โฆซ U+29AB block prefix 0 0 N/A โฆฌ U+29AC block prefix 0 0 N/A โฆญ U+29AD block prefix 0 0 N/A โฆฎ U+29AE block prefix 0 0 N/A โฆฏ U+29AF block prefix 0 0 N/A โซฌ U+2AEC block prefix 0 0 N/A โซญ U+2AED block prefix 0 0 N/A String || U+007C U+007C block prefix 0 0 fence ! U+0021 block postfix 0 0 N/A " U+0022 block postfix 0 0 N/A % U+0025 block postfix 0 0 N/A & U+0026 block postfix 0 0 N/A ' U+0027 block postfix 0 0 N/A ` U+0060 block postfix 0 0 N/A ยจ U+00A8 block postfix 0 0 N/A ยฐ U+00B0 block postfix 0 0 N/A ยฒ U+00B2 block postfix 0 0 N/A ยณ U+00B3 block postfix 0 0 N/A ยด U+00B4 block postfix 0 0 N/A ยธ U+00B8 block postfix 0 0 N/A ยน U+00B9 block postfix 0 0 N/A ห U+02CA block postfix 0 0 N/A ห U+02CB block postfix 0 0 N/A ห U+02D8 block postfix 0 0 N/A ห U+02D9 block postfix 0 0 N/A ห U+02DA block postfix 0 0 N/A ห U+02DD block postfix 0 0 N/A ฬ U+0311 block postfix 0 0 N/A โ U+2019 block postfix 0 0 fence โ U+201A block postfix 0 0 N/A โ U+201B block postfix 0 0 N/A โ U+201D block postfix 0 0 fence โ U+201E block postfix 0 0 N/A โ U+201F block postfix 0 0 N/A โฒ U+2032 block postfix 0 0 N/A โณ U+2033 block postfix 0 0 N/A โด U+2034 block postfix 0 0 N/A โต U+2035 block postfix 0 0 N/A โถ U+2036 block postfix 0 0 N/A โท U+2037 block postfix 0 0 N/A โ U+2057 block postfix 0 0 N/A โ U+20DB block postfix 0 0 N/A โ U+20DC block postfix 0 0 N/A โ U+23CD block postfix 0 0 N/A String !! U+0021 U+0021 block postfix 0 0 N/A String ++ U+002B U+002B block postfix 0 0 N/A String -- U+002D U+002D block postfix 0 0 N/A String || U+007C U+007C block postfix 0 0 fence ( U+0028 block prefix 0 0 stretchy symmetric fence [ U+005B block prefix 0 0 stretchy symmetric fence { U+007B block prefix 0 0 stretchy symmetric fence | U+007C block prefix 0 0 stretchy symmetric fence โ U+2016 block prefix 0 0 stretchy symmetric fence โ U+2308 block prefix 0 0 stretchy symmetric fence โ U+230A block prefix 0 0 stretchy symmetric fence โฉ U+2329 block prefix 0 0 stretchy symmetric fence โฒ U+2772 block prefix 0 0 stretchy symmetric fence โฆ U+27E6 block prefix 0 0 stretchy symmetric fence โจ U+27E8 block prefix 0 0 stretchy symmetric fence โช U+27EA block prefix 0 0 stretchy symmetric fence โฌ U+27EC block prefix 0 0 stretchy symmetric fence โฎ U+27EE block prefix 0 0 stretchy symmetric fence โฆ U+2980 block prefix 0 0 stretchy symmetric fence โฆ U+2983 block prefix 0 0 stretchy symmetric fence โฆ
U+2985 block prefix 0 0 stretchy symmetric fence โฆ U+2987 block prefix 0 0 stretchy symmetric fence โฆ U+2989 block prefix 0 0 stretchy symmetric fence โฆ U+298B block prefix 0 0 stretchy symmetric fence โฆ U+298D block prefix 0 0 stretchy symmetric fence โฆ U+298F block prefix 0 0 stretchy symmetric fence โฆ U+2991 block prefix 0 0 stretchy symmetric fence โฆ U+2993 block prefix 0 0 stretchy symmetric fence โฆ U+2995 block prefix 0 0 stretchy symmetric fence โฆ U+2997 block prefix 0 0 stretchy symmetric fence โฆ U+2999 block prefix 0 0 stretchy symmetric fence โง U+29D8 block prefix 0 0 stretchy symmetric fence โง U+29DA block prefix 0 0 stretchy symmetric fence โงผ U+29FC block prefix 0 0 stretchy symmetric fence ) U+0029 block postfix 0 0 stretchy symmetric fence ] U+005D block postfix 0 0 stretchy symmetric fence | U+007C block postfix 0 0 stretchy symmetric fence } U+007D block postfix 0 0 stretchy symmetric fence โ U+2016 block postfix 0 0 stretchy symmetric fence โ U+2309 block postfix 0 0 stretchy symmetric fence โ U+230B block postfix 0 0 stretchy symmetric fence โช U+232A block postfix 0 0 stretchy symmetric fence โณ U+2773 block postfix 0 0 stretchy symmetric fence โง U+27E7 block postfix 0 0 stretchy symmetric fence โฉ U+27E9 block postfix 0 0 stretchy symmetric fence โซ U+27EB block postfix 0 0 stretchy symmetric fence โญ U+27ED block postfix 0 0 stretchy symmetric fence โฏ U+27EF block postfix 0 0 stretchy symmetric fence โฆ U+2980 block postfix 0 0 stretchy symmetric fence โฆ U+2984 block postfix 0 0 stretchy symmetric fence โฆ U+2986 block postfix 0 0 stretchy symmetric fence โฆ U+2988 block postfix 0 0 stretchy symmetric fence โฆ U+298A block postfix 0 0 stretchy symmetric fence โฆ U+298C block postfix 0 0 stretchy symmetric fence โฆ U+298E block postfix 0 0 stretchy symmetric fence โฆ U+2990 block postfix 0 0 stretchy symmetric fence โฆ U+2992 block postfix 0 0 stretchy symmetric fence โฆ U+2994 block postfix 0 0 stretchy symmetric fence โฆ U+2996 block postfix 0 0 stretchy symmetric fence โฆ U+2998 block postfix 0 0 stretchy symmetric fence โฆ U+2999 block postfix 0 0 stretchy symmetric fence โง U+29D9 block postfix 0 0 stretchy symmetric fence โง U+29DB block postfix 0 0 stretchy symmetric fence โงฝ U+29FD block postfix 0 0 stretchy symmetric fence โซ U+222B block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โฌ U+222C block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โญ U+222D block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โฎ U+222E block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โฏ U+222F block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โฐ U+2230 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โฑ U+2231 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โฒ U+2232 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โณ U+2233 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A0B block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A0C block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A0D block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A0E block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A0F block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A10 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A11 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A12 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A13 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A14 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A15 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A16 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A17 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A18 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A19 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A1A block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A1B block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop โจ U+2A1C block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop ^ U+005E inline postfix 0 0 stretchy _ U+005F inline postfix 0 0 stretchy ~ U+007E inline postfix 0 0 stretchy ยฏ U+00AF inline postfix 0 0 stretchy ห U+02C6 inline postfix 0 0 stretchy ห U+02C7 inline postfix 0 0 stretchy ห U+02C9 inline postfix 0 0 stretchy ห U+02CD inline postfix 0 0 stretchy ห U+02DC inline postfix 0 0 stretchy หท U+02F7 inline postfix 0 0 stretchy ฬ U+0302 inline postfix 0 0 stretchy โพ U+203E inline postfix 0 0 stretchy โข U+2322 inline postfix 0 0 stretchy โฃ U+2323 inline postfix 0 0 stretchy โด U+23B4 inline postfix 0 0 stretchy โต U+23B5 inline postfix 0 0 stretchy โ U+23DC inline postfix 0 0 stretchy โ U+23DD inline postfix 0 0 stretchy โ U+23DE inline postfix 0 0 stretchy โ U+23DF inline postfix 0 0 stretchy โ U+23E0 inline postfix 0 0 stretchy โก U+23E1 inline postfix 0 0 stretchy ๐ปฐ U+1EEF0 inline postfix 0 0 stretchy ๐ปฑ U+1EEF1 inline postfix 0 0 stretchy โ U+220F block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โ U+2210 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โ U+2211 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โ U+22C0 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โ U+22C1 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โ U+22C2 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โ U+22C3 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A00 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A01 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A02 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A03 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A04 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ
U+2A05 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A06 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A07 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A08 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A09 block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A0A block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A1D block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โจ U+2A1E block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โซผ U+2AFC block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits โซฟ U+2AFF block prefix 0.16666666666666666em 0.16666666666666666em symmetric largeop movablelimits \ U+005C block infix 0 0 N/A _ U+005F inline infix 0 0 N/A โก U+2061 block infix 0 0 N/A โข U+2062 block infix 0 0 N/A โฃ U+2063 block infix 0 0 separator โค U+2064 block infix 0 0 N/A โ U+2206 block infix 0 0 N/A โ
U+2145 block prefix 0.16666666666666666em 0 N/A โ
U+2146 block prefix 0.16666666666666666em 0 N/A โ U+2202 block prefix 0.16666666666666666em 0 N/A โ U+221A block prefix 0.16666666666666666em 0 N/A โ U+221B block prefix 0.16666666666666666em 0 N/A โ U+221C block prefix 0.16666666666666666em 0 N/A , U+002C block infix 0 0.16666666666666666em separator : U+003A block infix 0 0.16666666666666666em N/A ; U+003B block infix 0 0.16666666666666666em separator Figure 29 Mapping from operator (Content, Form) to properties.This section is non-normative.
The following table gives mappings between spacing and non spacing characters when used in MathML accent constructs.
Non Combining Style Combining U+002B plus sign below U+031F combining plus sign below U+002D hyphen-minus above U+0305 combining overline U+002D hyphen-minus below U+0320 combining minus sign below U+002D hyphen-minus below U+0332 combining low line U+002E full stop above U+0307 combining dot above U+002E full stop below U+0323 combining dot below U+005E circumflex accent above U+0302 combining circumflex accent U+005E circumflex accent below U+032D combining circumflex accent below U+005F low line below U+0332 combining low line U+0060 grave accent above U+0300 combining grave accent U+0060 grave accent below U+0316 combining grave accent below U+007E tilde above U+0303 combining tilde U+007E tilde below U+0330 combining tilde below U+00A8 diaeresis above U+0308 combining diaeresis U+00A8 diaeresis below U+0324 combining diaeresis below U+00AF macron above U+0304 combining macron U+00AF macron above U+0305 combining overline U+00B4 acute accent above U+0301 combining acute accent U+00B4 acute accent below U+0317 combining acute accent below U+00B8 cedilla below U+0327 combining cedilla U+02C6 modifier letter circumflex accent above U+0302 combining circumflex accent U+02C7 caron above U+030C combining caron U+02C7 caron below U+032C combining caron below U+02D8 breve above U+0306 combining breve U+02D8 breve below U+032E combining breve below U+02D9 dot above above U+0307 combining dot above U+02D9 dot above below U+0323 combining dot below U+02DB ogonek below U+0328 combining ogonek U+02DC small tilde above U+0303 combining tilde U+02DC small tilde below U+0330 combining tilde below U+02DD double acute accent above U+030B combining double acute accent U+203E overline above U+0305 combining overline U+2190 leftwards arrow above U+20D6 U+2192 rightwards arrow above U+20D7 combining right arrow above U+2192 rightwards arrow above U+20EF combining right arrow below U+2212 minus sign above U+0305 combining overline U+2212 minus sign below U+0332 combining low line U+27F6 long rightwards arrow above U+20D7 combining right arrow above U+27F6 long rightwards arrow above U+20EF combining right arrow below Combining Style Non Combining U+0300 combining grave accent above U+0060 grave accent U+0301 combining acute accent above U+00B4 acute accent U+0302 combining circumflex accent above U+005E circumflex accent U+0302 combining circumflex accent above U+02C6 modifier letter circumflex accent U+0303 combining tilde above U+007E tilde U+0303 combining tilde above U+02DC small tilde U+0304 combining macron above U+00AF macron U+0305 combining overline above U+002D hyphen-minus U+0305 combining overline above U+00AF macron U+0305 combining overline above U+203E overline U+0305 combining overline above U+2212 minus sign U+0306 combining breve above U+02D8 breve U+0307 combining dot above above U+02E U+0307 combining dot above above U+002E full stop U+0307 combining dot above above U+02D9 dot above U+0308 combining diaeresis above U+00A8 diaeresis U+030B combining double acute accent above U+02DD double acute accent U+030C combining caron above U+02C7 caron U+0312 combining turned comma above above U+0B8 U+0316 combining grave accent below below U+0060 grave accent U+0317 combining acute accent below below U+00B4 acute accent U+031F combining plus sign below below U+002B plus sign U+0320 combining minus sign below below U+002D hyphen-minus U+0323 combining dot below below U+002E full stop U+0323 combining dot below below U+02D9 dot above U+0324 combining diaeresis below below U+00A8 diaeresis U+0327 combining cedilla below U+00B8 cedilla U+0328 combining ogonek below U+02DB ogonek U+032C combining caron below below U+02C7 caron U+032D combining circumflex accent below below U+005E circumflex accent U+032E combining breve below below U+02D8 breve U+0330 combining tilde below below U+007E tilde U+0330 combining tilde below below U+02DC small tilde U+0332 combining low line below U+002D hyphen-minus U+0332 combining low line below U+005F low line U+0332 combining low line below U+2212 minus sign U+0338 combining long solidus overlay over U+02F U+20D7 combining right arrow above above U+2192 rightwards arrow U+20D7 combining right arrow above above U+27F6 long rightwards arrow U+20EF combining right arrow below above U+2192 rightwards arrow U+20EF combining right arrow below above U+27F6 long rightwards arrowThis section is non-normative.
The following table provide fallback that user agents may use for stretching a given base character when the font does not provide a MATH.MathVariants table. The algorithms of 5.3 Size variants for operators (MathVariants) works the same except with some adjustments:
MathVariants.horizGlyphConstructionOffsets[] item ; if it is vertical it corresponds to a MathVariants.vertGlyphConstructionOffsets[] item.MathGlyphConstruction.mathGlyphVariantRecord is always empty.MathVariants.minConnectorOverlap, GlyphPartRecord.startConnectorLength and GlyphPartRecord.endConnectorLength are treated as 0.MathGlyphConstruction.GlyphAssembly.partRecords is built from each table row as follows:
This section is non-normative.
MathML Core is based on MathML3. See the appendix E of [MathML3] for the people that contributed to that specification.
We would like to thank the people who, through their input and feedback on public communication channels have helped us with the creation of this specification: Andrรฉ Greiner-Petter, Anne van Kesteren, Boris Zbarsky, Brian Smith, Daniel Marques, David Carlisle, Deyan Ginev, Elika Etemad, Emilio Cobos รlvarez, ExE Boss, Ian Kilpatrick, Koji Ishii, L. David Baron, Michael Kohlhase, Michael Smith, Moritz Schubotz, Murray Sargent, Ryosuke Niwa, Sergey Malkin, Tab Atkins Jr., Viktor Yaffle and frankvel.
In addition, we would like to extend special thanks to Brian Kardell, Neil Soiffer and Rob Buis for help with the editing.
Many thanks also to the following people for their help with the test suite: Brian Kardell, Frรฉdรฉric Wang, Neil Soiffer and Rob Buis. Several tests are also based on MathML tests from browser repositories and we are grateful to the Mozilla and WebKit contributors.
Community Group members who have regularly participated to MathML Core meetings during the development of this specification: Brian Kardell, Bruce Miller, David Carlisle, Murray Sargent, Frรฉdรฉric Wang, Neil Soiffer (Chair), Patrick Ion, Rob Buis, David Farmer, Steve Noble, Daniel Marques, Sam Dooley.
This section is non-normative.
This specification adds script execution mechanisms via the MathML event handler attributes described in 2.1.3 Global Attributes. UAs may decide to prevent execution of scripts specified in these attributes, following the same security restrictions as those applying to HTML or SVG elements.
Note
In [MathML3], it was possible to make any element linkable via href or xlink:href attributes, with an URL pointing to an untrusted resource or even javascript: execution. These attributes are not available in MathML Core. However, as described in 2.2.1 HTML and SVG it is possible to embed HTML or SVG content inside MathML, including HTML or SVG links.
Note
In [MathML3], it was possible to use the <maction>actiontype value set to "statusline" in order to override the text of the browser statusline. In particular, an attacker could use this to hide the URL text of an untrusted link e.g.
<math>
<maction actiontype="statusline">
<mtext><a href="javascript:alert('JS execution')">Click me!</a></mtext>
<mtext>./this-is-a-safe-link.html</mtext>
</maction>
</math>This feature is not available in MathML Core, where the <maction><mrow>
An attacker can try to hang the UA by inserting very large stretchy operators, effectively making the algorithm shaping of the glyph assembly deal with a huge amount of glyphs. UAs may work around this issue by limiting rmin and GlyphAssembly.partCount to maximum values.
As described in CSS Fonts Module, an attacker can try to rely on malformed or malicious fonts to exploit potential security faults in browser implementations. Because the OpenType MATH table is used extensively in this specification, UAs should ensure their font sanitization mechanisms are able to deal with that table.
Finally, in order to reduce attack surface, some UAs expose runtime options to disable part of the web platform. Disabling MathML layout can essentially be achieved by forcing elements in the DOM tree to be put in the HTML namespace and disabling 4. CSS Extensions for Math Layout.
This section is non-normative.
As explained in 2.2.1 HTML and SVG, MathML can be embedded into an SVG image via the <foreignObject> element which can thus be used in a <canvas> element. UA may decide to implement any measure to prevent potential information leakage such as tainting the canvas and returning a "SecurityError" DOMException when one tries to access the canvas' content via JavaScript APIs.
In the following example, the canvas image is set to the image of some MathML content with a HTML link to https://example.org/. It should not be possible for an attacker to determine whether that link was visited by reading pixels via context.getImageData. For more about links in MathML, see E. Security Considerations.
let svg = `
<svg xmlns="http://www.w3.org/2000/svg" width="100px" height="100px">
<foreignObject width="100" height="100"
requiredExtensions="http://www.w3.org/1998/Math/MathML">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<msqrt style="font-size: 25px">
<mtext>■</mtext>
<mtext><a href="https://example.org/">■</a></mtext>
</msqrt>
</math>
</foreignObject>
</svg>`;
let image = new Image();
image.width = 100;
image.height = 100;
image.onload = () => {
let canvas = document.createElement('canvas');
canvas.width = 100;
canvas.height = 100;
canvas.style = "border: 1px solid black";
document.body.appendChild(canvas);
let context = canvas.getContext("2d");
context.drawImage(image, 0, 0);
};
image.src = `data:image/svg+xml;base64,${window.btoa(svg)}`;This specification describes layout of a DOM elements which may involve system fonts. Like for HTML/CSS layout, it is thus possible to use JavaScript APIs (e.g. context.getImageData on content embedded in a canvas context, or even just getBoundingClientRect()) to measure box sizes and positions and infer data from system fonts. By combining miscelleneaous tests on such fonts and comparing measurements against results of well-known fonts, an attacker can try and determine the default fonts of the user.
The following HTML+CSS+JavaScript document relies on a Web font with exotic metrics to try and determine whether A Well Known System Font is available by default.
<style>
@font-face {
font-family: MyWebFontWithVeryWideGlyphs;
src: url("/fonts/my-web-fonts-with-very-wide-glyphs.woff");
}
#container {
font-family: AWellKnownSystemFont, MyWebFontWithVeryWideGlyphs;
}
</style>
<div id="container">SOMETEXT</div>
<div id="reference">SOMETEXT</div>
<script>
document.fonts.ready.then(() => {
let containerWidth =
document.getElementById("container").getBoundingClientRect().width;
let referenceWidth =
document.getElementById("reference").getBoundingClientRect().width;
let isWellKnownSystemFontAvailable =
Math.abs(containerWidth - referenceWidth) < 1;
});
</script>The following HTML+CSS+JavaScript document tries to determine whether the the UI serif font provide Asian glyphs:
<style>
@font-face {
font-family: MyWebFontWithVeryWideAsianGlyphs;
src: url("/fonts/my-web-fonts-with-very-wide-asian-glyphs.woff");
}
#container {
font-family: ui-serif, MyWebFontWithVeryWideAsianGlyphs
}
#reference {
font-family: MyWebFontWithVeryWideAsianGlyphs;
}
</style>
<div id="container">็</div>
<div id="reference">็</div>
<script>
document.fonts.ready.then(() => {
let containerWidth =
document.getElementById("container").getBoundingClientRect().width;
let referenceWidth =
document.getElementById("reference").getBoundingClientRect().width;
let uiSerifFontDoesNotContainAsianGlyph =
Math.abs(containerWidth - referenceWidth) < 1;
});
</script>The following HTML+CSS document contains the same text rendered with text-decoration-thickness set to from-font and 1em (here 100 pixels) respectively. By comparing the heights of the two under lines, one can calculate a good approximation of the underlineThickness value from the PostScript Table [OPEN-FONT-FORMAT].
<style>
#test {
font-size: 100px;
}
#container {
text-decoration-line: underline;
text-decoration-thickness: from-font;
}
#reference {
text-decoration-line: underline;
text-decoration-thickness: 1em;
}
</style>
<div id="test">
<div id="container">SOMETEXT</div>
<div id="reference">SOMETEXT</div>
</div>This specification relies on information from 5. OpenType MATH table to render MathML content. One can get good approximation of most layout parameters from MathConstants and MathGlyphInfo using measurement techniques similar to what is described above for HTML+CSS+JavaScript document. The use of the MathVariants table for MathML rendering can also be observed by putting stretchy operators of different sizes inside a canvas context.
Although none of these parameters taken individually are personal, implementing this specification increases the set of exposed font information that can be used by an attacker to implement fingerprinting techniques. Typically, they could help dermine available and preferred math fonts for a user.
As well as sections marked as non-normative, all authoring guidelines, diagrams, examples, and notes in this specification are non-normative. Everything else in this specification is normative.
The key words MAY, MUST, MUST NOT, OPTIONAL, RECOMMENDED, REQUIRED, SHALL, SHALL NOT, SHOULD, and SHOULD NOT in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.
Conformance requirements are expressed with a combination of descriptive assertions and RFC 2119 terminology. The key words โMUSTโ, โMUST NOTโ, โREQUIREDโ, โSHALLโ, โSHALL NOTโ, โSHOULDโ, โSHOULD NOTโ, โRECOMMENDEDโ, โMAYโ, and โOPTIONALโ in the normative parts of this document are to be interpreted as described in RFC 2119. However, for readability, these words do not appear in all uppercase letters in this specification.
All of the text of this specification is normative except sections explicitly marked as non-normative, examples, and notes. [RFC2119].
Examples in this specification are introduced with the words โfor exampleโ or are set apart from the normative text with class="example", like this:
This is an example of an informative example.
Informative notes begin with the word โNoteโ and are set apart from the normative text with class="note", like this:
Note
Note, this is an informative note.
Advisements are normative sections styled to evoke special attention and are set apart from other normative text with <strong class="advisement">, like this: UAs MUST provide an accessible alternative.
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